-
1
-
-
0033099830
-
Numerical study of approximate inverse preconditioner for two-dimensional engine inlet problems
-
C. H. Ahn, W. C. Chew, J. S. Zhao, and E. Michielssen, Numerical study of approximate inverse preconditioner for two-dimensional engine inlet problems, Electromagnetics 19, 131 (1999).
-
(1999)
Electromagnetics
, vol.19
, pp. 131
-
-
Ahn, C.H.1
Chew, W.C.2
Zhao, J.S.3
Michielssen, E.4
-
2
-
-
0021427797
-
A robust incomplete Choleski-conjugate gradient algorithm
-
M. A. Ajiz and A. Jennings, A robust incomplete Choleski-conjugate gradient algorithm, Int. J. Numer. Methods Eng. 20, 949 (1984).
-
(1984)
Int. J. Numer. Methods Eng.
, vol.20
, pp. 949
-
-
Ajiz, M.A.1
Jennings, A.2
-
3
-
-
0043234061
-
Sparse approximate inverse preconditioning for dense linear systems arising in computational electromagnetics
-
G. Alléon, M. Benzi, and L. Giraud, Sparse approximate inverse preconditioning for dense linear systems arising in computational electromagnetics, Numer. Algorithms 16, 1 (1997).
-
(1997)
Numer. Algorithms
, vol.16
, pp. 1
-
-
Alléon, G.1
Benzi, M.2
Giraud, L.3
-
4
-
-
0030491606
-
An approximate minimum degree ordering algorithm
-
P. Amestoy, T. A. Davis, and I. S. Duff, An approximate minimum degree ordering algorithm, SIAM J. Matrix Anal. Appl. 17, 886 (1996).
-
(1996)
SIAM J. Matrix Anal. Appl.
, vol.17
, pp. 886
-
-
Amestoy, P.1
Davis, T.A.2
Duff, I.S.3
-
5
-
-
0036060795
-
A fully asynchronous multifrontal solver using distributed dynamic scheduling
-
P. Amestoy, I. S. Duff, J.-Y. L'Excellent, and J. Koster, A fully asynchronous multifrontal solver using distributed dynamic scheduling, SIAM J. Matrix Anal. Appl. 23, 15 (2001).
-
(2001)
SIAM J. Matrix Anal. Appl.
, vol.23
, pp. 15
-
-
Amestoy, P.1
Duff, I.S.2
L'Excellent, J.-Y.3
Koster, J.4
-
6
-
-
0000262046
-
A linear algebraic analysis of diffusion synthetic acceleration for the Boltzmann transport equation
-
S. F. Ashby, P. N. Brown, M. R. Dorr, and A. C. Hindmarsh, A linear algebraic analysis of diffusion synthetic acceleration for the Boltzmann transport equation, SIAM J. Numer. Anal. 32, 179 (1995).
-
(1995)
SIAM J. Numer. Anal.
, vol.32
, pp. 179
-
-
Ashby, S.F.1
Brown, P.N.2
Dorr, M.R.3
Hindmarsh, A.C.4
-
7
-
-
0001581067
-
Adaptive polynomial preconditioning for hermitian indefinite linear systems
-
S. F. Ashby, T. A. Manteuffel, and P. E. Saylor, Adaptive polynomial preconditioning for hermitian indefinite linear systems, BIT 29, 583 (1989).
-
(1989)
BIT
, vol.29
, pp. 583
-
-
Ashby, S.F.1
Manteuffel, T.A.2
Saylor, P.E.3
-
8
-
-
0000729339
-
Compressed graphs and the minimum degree algorithm
-
C. Ashcraft, Compressed graphs and the minimum degree algorithm, SIAM J. Sci. Comput. 16, 1404 (1995).
-
(1995)
SIAM J. Sci. Comput.
, vol.16
, pp. 1404
-
-
Ashcraft, C.1
-
9
-
-
0001160426
-
A generalized SSOR method
-
O. Axelsson, A generalized SSOR method, BIT 13, 443 (1972).
-
(1972)
BIT
, vol.13
, pp. 443
-
-
Axelsson, O.1
-
10
-
-
0021825930
-
A survey of preconditioned iterative methods for linear systems of algebraic equations
-
O. Axelsson, A survey of preconditioned iterative methods for linear systems of algebraic equations, BIT 25, 166 (1985).
-
(1985)
BIT
, vol.25
, pp. 166
-
-
Axelsson, O.1
-
11
-
-
38249042495
-
A general incomplete block matrix factorization method
-
O. Axelsson, A general incomplete block matrix factorization method, Linear Algebra Its Appl. 74, 179 (1986).
-
(1986)
Linear Algebra Its Appl.
, vol.74
, pp. 179
-
-
Axelsson, O.1
-
12
-
-
0004100224
-
Iterative Solution Methods
-
(Cambridge Univ. Press, Cambridge)
-
O. Axelsson, Iterative Solution Methods (Cambridge Univ. Press, Cambridge, 1994).
-
(1994)
-
-
Axelsson, O.1
-
13
-
-
0002622213
-
On some versions of incomplete block matrix factorization iterative methods
-
O. Axelsson, S. Brinkkemper, and V. P. Il'in, On some versions of incomplete block matrix factorization iterative methods, Linear Algebra Its Appl. 58, 3 (1984).
-
(1984)
Linear Algebra Its Appl.
, vol.58
, pp. 3
-
-
Axelsson, O.1
Brinkkemper, S.2
Il'in, V.P.3
-
14
-
-
38249006029
-
Vectorizable preconditioners for elliptic difference equations in three space dimensions
-
O. Axelsson and V. Eijkhout, Vectorizable preconditioners for elliptic difference equations in three space dimensions, J. Comput. Appl. Math. 27, 299 (1991).
-
(1991)
J. Comput. Appl. Math.
, vol.27
, pp. 299
-
-
Axelsson, O.1
Eijkhout, V.2
-
15
-
-
84985315720
-
Diagonally compensated reduction and related preconditioning methods
-
O. Axelsson and L. Yu. Kolotilina, Diagonally compensated reduction and related preconditioning methods, Numer. Linear Algebra Appl. 1, 155 (1994).
-
(1994)
Numer. Linear Algebra Appl.
, vol.1
, pp. 155
-
-
Axelsson, O.1
Kolotilina, L.Yu.2
-
16
-
-
0000779223
-
Algebraic multilevel preconditioning methods, I
-
O. Axelsson and P. S. Vassilevski, Algebraic multilevel preconditioning methods, I, Numer. Math. 56, 157 (1989).
-
(1989)
Numer. Math.
, vol.56
, pp. 157
-
-
Axelsson, O.1
Vassilevski, P.S.2
-
17
-
-
0001573921
-
Algebraic multilevel preconditioning methods, II
-
O. Axelsson and P. S. Vassilevski, Algebraic multilevel preconditioning methods, II, SIAM J. Numer. Anal. 27, 1569 (1990).
-
(1990)
SIAM J. Numer. Anal.
, vol.27
, pp. 1569
-
-
Axelsson, O.1
Vassilevski, P.S.2
-
18
-
-
0003660984
-
-
Report ANL 95/11, Revision 2.2.3 (Argonne National Laboratory, Argonne, IL)
-
S. Balay, K. Buschelman, W. Gropp, D. Kaushik, M. Knepley, L. C. McInnes, B. Smith, and H. Zhang, PETSc User's Manual, Report ANL 95/11, Revision 2.2.3 (Argonne National Laboratory, Argonne, IL, 2002).
-
(2002)
PETSc User's Manual
-
-
Balay, S.1
Buschelman, K.2
Gropp, W.3
Kaushik, D.4
Knepley, M.5
McInnes, L.C.6
Smith, B.7
Zhang, H.8
-
19
-
-
0000676005
-
An approximate inverse based multigrid approach to the biharmonic problem
-
R. N. Banerjee and M. W. Benson, An approximate inverse based multigrid approach to the biharmonic problem, Int. J. Comput. Math. 40, 201 (1991).
-
(1991)
Int. J. Comput. Math.
, vol.40
, pp. 201
-
-
Banerjee, R.N.1
Benson, M.W.2
-
20
-
-
0033279293
-
The incomplete factorization multigraph algorithm
-
R. E. Bank and R. K. Smith, The incomplete factorization multigraph algorithm, SIAM J. Sci. Comput. 20, 1349 (1999).
-
(1999)
SIAM J. Sci. Comput.
, vol.20
, pp. 1349
-
-
Bank, R.E.1
Smith, R.K.2
-
21
-
-
0036982605
-
An algebraic multilevel multigraph algorithm
-
R. E. Bank and R. K. Smith, An algebraic multilevel multigraph algorithm, SIAM J. Sci. Comput. 23, 1572 (2002).
-
(2002)
SIAM J. Sci. Comput.
, vol.23
, pp. 1572
-
-
Bank, R.E.1
Smith, R.K.2
-
22
-
-
0033433038
-
Multilevel ILU decomposition
-
R. E. Bank and C. Wagner, Multilevel ILU decomposition, Numer. Math. 82, 543 (1999).
-
(1999)
Numer. Math.
, vol.82
, pp. 543
-
-
Bank, R.E.1
Wagner, C.2
-
23
-
-
0032630275
-
An MPI implementation of the SPAI preconditioner on the T3E
-
S. T. Barnard, L. M. Bernardo, and H. D. Simon, An MPI implementation of the SPAI preconditioner on the T3E, Int. J. High Perform. Comput. Appl. 13, 107 (1999).
-
(1999)
Int. J. High Perform. Comput. Appl.
, vol.13
, pp. 107
-
-
Barnard, S.T.1
Bernardo, L.M.2
Simon, H.D.3
-
24
-
-
0012122551
-
A portable MPI implementation of the SPAI preconditioner in ISIS++
-
Proceedings of the Eight SIAM Conference on Parallel Processing for Scientific Computing, edited by M. Heath et al. (SIAM, Philadelphia, PA, [CD-ROM])
-
S. T. Barnard and R. L. Clay, A portable MPI implementation of the SPAI preconditioner in ISIS++, in Proceedings of the Eight SIAM Conference on Parallel Processing for Scientific Computing, edited by M. Heath et al. (SIAM, Philadelphia, PA, 1997 [CD-ROM]).
-
(1997)
-
-
Barnard, S.T.1
Clay, R.L.2
-
25
-
-
0012200017
-
A block version of the SPAI preconditioner
-
Proceedings of the Ninth SIAM Conference on Parallel Processing for Scientific Computing, edited by B. A. Hendrickson et al. (SIAM, Philadelphia, PA, [CD-ROM])
-
S. T. Barnard and M. J. Grote, A block version of the SPAI preconditioner, in Proceedings of the Ninth SIAM Conference on Parallel Processing for Scientific Computing, edited by B. A. Hendrickson et al. (SIAM, Philadelphia, PA, 1999 [CD-ROM]).
-
(1999)
-
-
Barnard, S.T.1
Grote, M.J.2
-
26
-
-
0003473816
-
Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods
-
(SIAM, Philadelphia, PA)
-
R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, Philadelphia, PA, 1994).
-
(1994)
-
-
Barrett, R.1
Berry, M.2
Chan, T.F.3
Demmel, J.4
Donato, J.5
Dongarra, J.6
Eijkhout, V.7
Pozo, R.8
Romine, C.9
van der Vorst, H.10
-
27
-
-
0002812224
-
Comparison of fast iterative methods for symmetric systems
-
G. A. Behie and P. A. Forsyth, Comparison of fast iterative methods for symmetric systems, IMA J. Numer. Anal. 3, 41 (1983).
-
(1983)
IMA J. Numer. Anal.
, vol.3
, pp. 41
-
-
Behie, G.A.1
Forsyth, P.A.2
-
28
-
-
0003884376
-
Iterative Solution of Large Scale Linear Systems
-
M.Sc. thesis (Lakehead University, Thunder Bay, Ontario)
-
M. W. Benson, Iterative Solution of Large Scale Linear Systems, M.Sc. thesis (Lakehead University, Thunder Bay, Ontario, 1973).
-
(1973)
-
-
Benson, M.W.1
-
29
-
-
0002483812
-
Frequency domain behavior of a set of parallel multigrid smoothing operators
-
M. W. Benson, Frequency domain behavior of a set of parallel multigrid smoothing operators, Int. J. Comput. Math. 36, 77 (1990).
-
(1990)
Int. J. Comput. Math.
, vol.36
, pp. 77
-
-
Benson, M.W.1
-
30
-
-
85190812900
-
An approximate inverse based multigrid approach to thin domain problems
-
M. W. Benson, An approximate inverse based multigrid approach to thin domain problems, Util. Math. 45, 39 (1994).
-
(1994)
Util. Math.
, vol.45
, pp. 39
-
-
Benson, M.W.1
-
31
-
-
0000131670
-
Iterative solution of large sparse linear systems arising in certain multidimensional approximation problems
-
M. W. Benson and P. O. Frederickson, Iterative solution of large sparse linear systems arising in certain multidimensional approximation problems, Util. Math. 22, 127 (1982).
-
(1982)
Util. Math.
, vol.22
, pp. 127
-
-
Benson, M.W.1
Frederickson, P.O.2
-
32
-
-
0034889465
-
Robust approximate inverse preconditioning for the conjugate gradient method
-
M. Benzi, J. K. Cullum, and M. Tůma, Robust approximate inverse preconditioning for the conjugate gradient method, SIAM J. Sci. Comput. 22, 1318 (2000).
-
(2000)
SIAM J. Sci. Comput.
, vol.22
, pp. 1318
-
-
Benzi, M.1
Cullum, J.K.2
Tůma, M.3
-
33
-
-
0034884436
-
Preconditioning highly indefinite and nonsymmetric matrices
-
M. Benzi, J. C. Haws, and M. Tůma, Preconditioning highly indefinite and nonsymmetric matrices, SIAM J. Sci. Comput. 22, 1333 (2000).
-
(2000)
SIAM J. Sci. Comput.
, vol.22
, pp. 1333
-
-
Benzi, M.1
Haws, J.C.2
Tůma, M.3
-
34
-
-
0002599076
-
Numerical experiments with parallel orderings for ILU preconditioners
-
M. Benzi, W. D. Joubert, and G. Mateescu, Numerical experiments with parallel orderings for ILU preconditioners, Electron. Trans. Numer. Anal. 8, 88 (1999).
-
(1999)
Electron. Trans. Numer. Anal.
, vol.8
, pp. 88
-
-
Benzi, M.1
Joubert, W.D.2
Mateescu, G.3
-
35
-
-
0032180742
-
An assessment of some preconditioning techniques in shell problems
-
M. Benzi, R. Kouhia, and M. Tůma, An assessment of some preconditioning techniques in shell problems, Commun. Numer. Methods Eng. 14, 897 (1998).
-
(1998)
Commun. Numer. Methods Eng.
, vol.14
, pp. 897
-
-
Benzi, M.1
Kouhia, R.2
Tůma, M.3
-
36
-
-
0035850685
-
Stabilized and block approximate inverse preconditioners for problems in solid and structural mechanics
-
M. Benzi, R. Kouhia, and M. Tůma, Stabilized and block approximate inverse preconditioners for problems in solid and structural mechanics, Comput. Methods Appl. Mech. Eng. 190, 6533 (2001).
-
(2001)
Comput. Methods Appl. Mech. Eng.
, vol.190
, pp. 6533
-
-
Benzi, M.1
Kouhia, R.2
Tůma, M.3
-
37
-
-
0000133360
-
A two-level parallel preconditioner based on sparse approximate inverses
-
IMACS Series in Computational and Applied Mathematics edited by D. R. Kincaid and A. C. Elster, (IMACS, New Brunswick, NJ)
-
M. Benzi, J. Marín, and M. Tůma, A two-level parallel preconditioner based on sparse approximate inverses, in Iterative Methods in Scientific Computation IV, edited by D. R. Kincaid and A. C. Elster, IMACS Series in Computational and Applied Mathematics, Vol. 5, p. 167. (IMACS, New Brunswick, NJ, 1999).
-
(1999)
Iterative Methods in Scientific Computation IV
, vol.5
, pp. 167
-
-
Benzi, M.1
Marín, J.2
Tůma, M.3
-
38
-
-
0004675411
-
A sparse approximate inverse preconditioner for the conjugate gradient method
-
M. Benzi, C. D. Meyer, and M. Tůma, A sparse approximate inverse preconditioner for the conjugate gradient method, SIAM J. Sci. Comput. 17, 1135 (1996).
-
(1996)
SIAM J. Sci. Comput.
, vol.17
, pp. 1135
-
-
Benzi, M.1
Meyer, C.D.2
Tůma, M.3
-
39
-
-
0033293791
-
Orderings for incomplete factorization preconditioning of nonsymmetric problems
-
M. Benzi, D. B. Szyld, and A. van Duin, Orderings for incomplete factorization preconditioning of nonsymmetric problems, SIAM J. Sci. Comput. 20, 1652 (1999).
-
(1999)
SIAM J. Sci. Comput.
, vol.20
, pp. 1652
-
-
Benzi, M.1
Szyld, D.B.2
van Duin, A.3
-
40
-
-
0001135947
-
A sparse approximate inverse preconditioner for nonsymmetric linear systems
-
M. Benzi and M. Tůma, A sparse approximate inverse preconditioner for nonsymmetric linear systems, SIAM J. Sci. Comput. 19, 968 (1998).
-
(1998)
SIAM J. Sci. Comput.
, vol.19
, pp. 968
-
-
Benzi, M.1
Tůma, M.2
-
41
-
-
0001635061
-
Numerical experiments with two approximate inverse preconditioners
-
M. Benzi and M. Tůma, Numerical experiments with two approximate inverse preconditioners, BIT 38, 234 (1998).
-
(1998)
BIT
, vol.38
, pp. 234
-
-
Benzi, M.1
Tůma, M.2
-
42
-
-
0033149240
-
A comparative study of sparse approximate inverse preconditioners
-
M. Benzi and M. Tůma, A comparative study of sparse approximate inverse preconditioners, Appl. Numer. Math. 30, 305 (1999).
-
(1999)
Appl. Numer. Math.
, vol.30
, pp. 305
-
-
Benzi, M.1
Tůma, M.2
-
43
-
-
18844471650
-
Orderings for factorized approximate inverse preconditioners
-
M. Benzi and M. Tůma, Orderings for factorized approximate inverse preconditioners, SIAM J. Sci. Comput. 21, 1851 (2000).
-
(2000)
SIAM J. Sci. Comput.
, vol.21
, pp. 1851
-
-
Benzi, M.1
Tůma, M.2
-
44
-
-
0013532162
-
A robust incomplete factorization preconditioner for positive definite matrices
-
in press
-
M. Benzi and M. Tůma, A robust incomplete factorization preconditioner for positive definite matrices, Numer. Linear Algebra Appl., in press.
-
Numer. Linear Algebra Appl.
-
-
Benzi, M.1
Tůma, M.2
-
45
-
-
0036533049
-
A parallel solver for large-scale Markov chains
-
M. Benzi and M. Tůma, A parallel solver for large-scale Markov chains, Appl. Numer. Math. 41, 135 (2002).
-
(2002)
Appl. Numer. Math.
, vol.41
, pp. 135
-
-
Benzi, M.1
Tůma, M.2
-
46
-
-
0034385436
-
Approximate inverse preconditioning in the parallel solution of sparse eigenproblems
-
L. Bergamaschi, G. Pini, and F. Sartoretto, Approximate inverse preconditioning in the parallel solution of sparse eigenproblems, Numer. Linear Algebra Appl. 7, 99 (2000).
-
(2000)
Numer. Linear Algebra Appl.
, vol.7
, pp. 99
-
-
Bergamaschi, L.1
Pini, G.2
Sartoretto, F.3
-
47
-
-
0035371089
-
Parallel preconditioning of a sparse eigensolver
-
L. Bergamaschi, G. Pini, and F. Sartoretto, Parallel preconditioning of a sparse eigensolver, Parallel Comput. 27, 963 (2001).
-
(2001)
Parallel Comput.
, vol.27
, pp. 963
-
-
Bergamaschi, L.1
Pini, G.2
Sartoretto, F.3
-
48
-
-
0003658403
-
-
3rd ed. (Academic Press, New York, 1979; reprinted by SIAM, Philadelphia, PA)
-
A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, 3rd ed. (Academic Press, New York, 1979; reprinted by SIAM, Philadelphia, PA, 1994).
-
(1994)
Nonnegative Matrices in the Mathematical Sciences
-
-
Berman, A.1
Plemmons, R.J.2
-
49
-
-
85009040419
-
Support graph preconditioners
-
submitted for publication
-
M. Bern, J. R. Gilbert, B. Hendrickson, N. Nguyen, and S. Toledo, Support graph preconditioners, submitted for publication.
-
-
-
Bern, M.1
Gilbert, J.R.2
Hendrickson, B.3
Nguyen, N.4
Toledo, S.5
-
50
-
-
0004171968
-
-
2nd ed. (Interscience, New York/North-Holland, Amsterdam)
-
E. Bodewig, Matrix Calculus, 2nd ed. (Interscience, New York/North-Holland, Amsterdam, 1959).
-
(1959)
Matrix Calculus
-
-
Bodewig, E.1
-
51
-
-
0035889740
-
A robust ILU with pivoting based on monitoring the growth of the inverse factors
-
M. Bollhöfer, A robust ILU with pivoting based on monitoring the growth of the inverse factors, Linear Algebra Its Appl. 338, 201 (2001).
-
(2001)
Linear Algebra Its Appl.
, vol.338
, pp. 201
-
-
Bollhöfer, M.1
-
52
-
-
85190801543
-
A robust and efficient ILU that incorporates the growth of the inverse triangular factors
-
submitted for publication
-
M. Bollhöfer, A robust and efficient ILU that incorporates the growth of the inverse triangular factors, submitted for publication.
-
-
-
Bollhöfer, M.1
-
53
-
-
0037281568
-
Algebraic multilevel methods and sparse approximate inverses
-
M. Bollhöfer and V. Mehrmann, Algebraic multilevel methods and sparse approximate inverses, SIAM J. Matrix Anal. Appl. 24, 191 (2002).
-
(2002)
SIAM J. Matrix Anal. Appl.
, vol.24
, pp. 191
-
-
Bollhöfer, M.1
Mehrmann, V.2
-
54
-
-
0036018632
-
A factored approximate inverse preconditioner with pivoting
-
M. Bollhöfer and Y. Saad, A factored approximate inverse preconditioner with pivoting, SIAM J. Matrix Anal. Appl. 23, 692 (2002).
-
(2002)
SIAM J. Matrix Anal. Appl.
, vol.23
, pp. 692
-
-
Bollhöfer, M.1
Saad, Y.2
-
55
-
-
0037288882
-
On the relations between ILUs and factored approximate inverses
-
M. Bollhöfer and Y. Saad, On the relations between ILUs and factored approximate inverses, SIAM J. Matrix Anal. Appl, 24, 219 (2002).
-
(2002)
SIAM J. Matrix Anal. Appl.
, vol.24
, pp. 19
-
-
Bollhöfer, M.1
Saad, Y.2
-
56
-
-
85190812479
-
Maximum-weigbt-basis preconditioners
-
submitted for publication
-
E. G. Boman, D. Chen, B. Hendrickson, and S. Toledo, Maximum-weigbt-basis preconditioners, submitted for publication.
-
-
-
Boman, E.G.1
Chen, D.2
Hendrickson, B.3
Toledo, S.4
-
57
-
-
0032625510
-
Preconditioned generalized minimal residual iterative scheme for perfectly matched layer terminated applications
-
Y. Y. Botros and J. L. Volakis, Preconditioned generalized minimal residual iterative scheme for perfectly matched layer terminated applications, IEEE Microwave Guided Wave Lett. 9, 45 (1999).
-
(1999)
IEEE Microwave Guided Wave Lett.
, vol.9
, pp. 45
-
-
Botros, Y.Y.1
Volakis, J.L.2
-
58
-
-
0033242225
-
Matrix renumbering ILU: An effective algebraic multilevel ILU preconditioner for sparse matrices
-
E. F. F. Botta and F. W. Wubs, Matrix renumbering ILU: An effective algebraic multilevel ILU preconditioner for sparse matrices, SIAM J. Matrix Anal. Appl. 20, 1007 (1999).
-
(1999)
SIAM J. Matrix Anal. Appl.
, vol.20
, pp. 1007
-
-
Botta, E.F.F.1
Wubs, F.W.2
-
59
-
-
0004219794
-
Multigrid Methods
-
(Longman Scientific & Technical, Harlow, UK)
-
J. H. Bramble, Multigrid Methods (Longman Scientific & Technical, Harlow, UK, 1993).
-
(1993)
-
-
Bramble, J.H.1
-
60
-
-
0001089735
-
An incomplete factorization preconditioning using repeated red/black ordering
-
C. W. Brand, An incomplete factorization preconditioning using repeated red/black ordering, Numer. Math. 61, 433 (1992).
-
(1992)
Numer. Math.
, vol.61
, pp. 433
-
-
Brand, C.W.1
-
61
-
-
84966233568
-
Multi-level adaptive solutions to boundary-value problems
-
A. Brandt, Multi-level adaptive solutions to boundary-value problems, Math. Comput. 31, 333 (1977).
-
(1977)
Math. Comput.
, vol.31
, pp. 333
-
-
Brandt, A.1
-
62
-
-
0002438068
-
Algebraic multigrid (AMG) for sparse matrix equations
-
edited by D. J. Evans, (Cambridge Univ. Press, Cambridge, UK)
-
A. Brandt, S. McCormick, and J. Ruge, Algebraic multigrid (AMG) for sparse matrix equations, in Sparsity and Its Applications, edited by D. J. Evans, p. 257 (Cambridge Univ. Press, Cambridge, UK, 1985).
-
(1985)
Sparsity and Its Applications
, pp. 257
-
-
Brandt, A.1
McCormick, S.2
Ruge, J.3
-
63
-
-
0003866523
-
Projection Methods for Systems of Equations, Studies in Computational Mathematics
-
(North-Holland, Amsterdam)
-
C. Brezinski, Projection Methods for Systems of Equations, Studies in Computational Mathematics, Vol. 27 (North-Holland, Amsterdam, 1997).
-
(1997)
, vol.27
-
-
Brezinski, C.1
-
64
-
-
0033295138
-
Ordering, anisotropy and factored sparse approximate inverses
-
R. Bridson and W.-P. Tang, Ordering, anisotropy and factored sparse approximate inverses, SIAM J. Sci. Comput. 21, 867 (1999),
-
(1999)
SIAM J. Sci. Comput.
, vol.21
, pp. 867
-
-
Bridson, R.1
Tang, W.-P.2
-
65
-
-
0034757965
-
A structural diagnosis of some IC orderings
-
R. Bridson and W.-P. Tang, A structural diagnosis of some IC orderings, SIAM J. Sci. Comput. 22, 1527 (2000).
-
(2000)
SIAM J. Sci. Comput.
, vol.22
, pp. 1527
-
-
Bridson, R.1
Tang, W.-P.2
-
67
-
-
0036223101
-
Multiresolution approximate inverse preconditioners
-
R. Bridson and W.-P. Tang, Multiresolution approximate inverse preconditioners, SIAM J. Sci. Comput. 23, 463 (2001),
-
(2001)
SIAM J. Sci. Comput.
, vol.23
, pp. 463
-
-
Bridson, R.1
Tang, W.-P.2
-
68
-
-
0004185470
-
-
2nd ed. (SIAM, Philadelphia, PA)
-
W. L. Briggs, V. E. Henson, and S. F. McCormick, A Multigrid Tutorial, 2nd ed. (SIAM, Philadelphia, PA, 2000).
-
(2000)
A Multigrid Tutorial
-
-
Briggs, W.L.1
Henson, V.E.2
McCormick, S.F.3
-
69
-
-
0036532991
-
Sparse approximate inverse smoothers for geometric and algebraic multigrid
-
O. Bröker and M. J. Grote. Sparse approximate inverse smoothers for geometric and algebraic multigrid, Appl. Numer. Math, 41, 61 (2002).
-
(2002)
Appl. Numer. Math,
, vol.41
, pp. 61
-
-
Bröker, O.1
Grote, M.J.2
-
70
-
-
0036348114
-
Robust parallel smoothing for multigrid via sparse approximate inverses
-
O. Bröker, M. J. Grote, C. Mayer, and A. Reusken, Robust parallel smoothing for multigrid via sparse approximate inverses, SIAM J. Sci. Comput. 23, 1395 (2001).
-
(2001)
SIAM J. Sci. Comput.
, vol.23
, pp. 1395
-
-
Bröker, O.1
Grote, M.J.2
Mayer, C.3
Reusken, A.4
-
71
-
-
0003541860
-
A Survey of Preconditioned Iterative Methods
-
(Longman Scientific & Technical, Harlow, UK)
-
A. M. Bruaset, A Survey of Preconditioned Iterative Methods (Longman Scientific & Technical, Harlow, UK, 1995).
-
(1995)
-
-
Bruaset, A.M.1
-
72
-
-
0012159376
-
A numerical method for solving two dimensional diffusion equations
-
[in Russian]
-
N. I. Buleev, A numerical method for solving two dimensional diffusion equations, At. Energ. 6, 338 (1959) [in Russian].
-
(1959)
At. Energ.
, vol.6
, pp. 338
-
-
Buleev, N.I.1
-
73
-
-
0001045889
-
A numerical method for solving two- and three-dimensional diffusion equations
-
[in Russian]
-
N. I. Buleev, A numerical method for solving two- and three-dimensional diffusion equations, Mat. Sb. 51, 227 (1960) [in Russian].
-
(1960)
Mat. Sb.
, vol.51
, pp. 227
-
-
Buleev, N.I.1
-
74
-
-
0034359574
-
Sparse pattern selection strategies for robust Frobenius-norm minimization preconditioners in electromagnetics
-
B. Carpentieri, I. S. Duff, and L. Giraud, Sparse pattern selection strategies for robust Frobenius-norm minimization preconditioners in electromagnetics, Numer. Linear Algebra Appl. 7, 667 (2000).
-
(2000)
Numer. Linear Algebra Appl.
, vol.7
, pp. 667
-
-
Carpentieri, B.1
Duff, I.S.2
Giraud, L.3
-
75
-
-
4243907622
-
Sparse Symmetric Preconditioners for Dense Linear Systems in Electromagnetics
-
CERFACS Technical Report TR/PA/01/35 (Toulouse, France)
-
B. Carpentieri, I. S. Duff, L. Giraud, and M. Magolu monga Made, Sparse Symmetric Preconditioners for Dense Linear Systems in Electromagnetics, CERFACS Technical Report TR/PA/01/35 (Toulouse, France, 2001).
-
(2001)
-
-
Carpentieri, B.1
Duff, I.S.2
Giraud, L.3
Magolu monga Made, M.4
-
76
-
-
2342644276
-
Combining fast multipole techniques and approximate inverse preconditioners for large calculations in electromagnetism
-
in Activity Report of the Parallel Algorithms Project at CERFACS, January 2001-December2001, CERFACS Tecnical Report TR/PA/01/105 (Toulouse, France)
-
B. Carpentieri, I. S. Duff, L. Giraud, and G. Sylvand, Combining fast multipole techniques and approximate inverse preconditioners for large calculations in electromagnetism, in Activity Report of the Parallel Algorithms Project at CERFACS, January 2001-December2001, CERFACS Tecnical Report TR/PA/01/105 (Toulouse, France, 2001).
-
(2001)
-
-
Carpentieri, B.1
Duff, I.S.2
Giraud, L.3
Sylvand, G.4
-
77
-
-
0001348998
-
Sulla risoluzione dei sistemi di equazioni lineari per approssimazioni successive
-
L. Cesari, Sulla risoluzione dei sistemi di equazioni lineari per approssimazioni successive, Atti Accad. Nazionale Lincei R. Classe Sci. Fis. Mat. Nat. 25, 422 (1937).
-
(1937)
Atti Accad. Nazionale Lincei R. Classe Sci. Fis. Mat. Nat.
, vol.25
, pp. 422
-
-
Cesari, L.1
-
78
-
-
0001514496
-
A simplified density matrix minimization for linear scaling self-consistent field theory
-
M. Challacombe, A simplified density matrix minimization for linear scaling self-consistent field theory, J. Chem. Phys. 110, 2332 (1999).
-
(1999)
J. Chem. Phys.
, vol.110
, pp. 2332
-
-
Challacombe, M.1
-
79
-
-
0034625292
-
A general parallel sparse-blocked matrix multiply for linear scaling SCF theory
-
M. Challacombe, A general parallel sparse-blocked matrix multiply for linear scaling SCF theory, Comput. Phys. Commun. 128, 93 (2000).
-
(2000)
Comput. Phys. Commun.
, vol.128
, pp. 93
-
-
Challacombe, M.1
-
80
-
-
0001238648
-
Wavelet sparse approximate inverse preconditioners
-
T. F. Chan, W.-P. Tang, and W.-L. Wan, Wavelet sparse approximate inverse preconditioners, BIT 37, 644 (1997).
-
(1997)
BIT
, vol.37
, pp. 644
-
-
Chan, T.F.1
Tang, W.-P.2
Wan, W.-L.3
-
81
-
-
0000005885
-
Approximate and incomplete factorizations
-
edited by D. E. Keyes, A. Sameh, and V. Venkatakrishnan, ICASE/LaRC Interdisciplinary Series in Science and Engineering, (Kluwer Academic, Dordrecht)
-
T. F. Chan and H. A. van der Vorst, Approximate and incomplete factorizations, in Parallel Numerical Algorithms, edited by D. E. Keyes, A. Sameh, and V. Venkatakrishnan, ICASE/LaRC Interdisciplinary Series in Science and Engineering, Vol. 4, p. 167 (Kluwer Academic, Dordrecht, 1997).
-
(1997)
Parallel Numerical Algorithms
, vol.4
, pp. 167
-
-
Chan, T.F.1
van der Vorst, H.A.2
-
82
-
-
0034233693
-
High-order ILU preconditioners for CFD problems
-
A. Chapman, Y. Saad, and L. Wigton, High-order ILU preconditioners for CFD problems, Int. J. Numer. Methods Fluids 33, 767 (2000).
-
(2000)
Int. J. Numer. Methods Fluids
, vol.33
, pp. 767
-
-
Chapman, A.1
Saad, Y.2
Wigton, L.3
-
83
-
-
85190791699
-
Vaidya's preconditioners: Implementation and experimental study
-
submitted for publication
-
D. Chen and S. Toledo, Vaidya's preconditioners: implementation and experimental study, submitted for publication.
-
-
-
Chen, D.1
Toledo, S.2
-
84
-
-
0032228601
-
On a class of preconditioning methods for dense linear systems from boundary elements
-
K. Chen, On a class of preconditioning methods for dense linear systems from boundary elements, SIAM J. Sci. Comput. 20, 684 (1998).
-
(1998)
SIAM J. Sci. Comput.
, vol.20
, pp. 684
-
-
Chen, K.1
-
85
-
-
0001684372
-
Discrete wavelet transforms accelerated sparse preconditioners for dense boundary element systems
-
K. Chen, Discrete wavelet transforms accelerated sparse preconditioners for dense boundary element systems, Electron. Trans. Numer. Anal. 8, 138 (1999).
-
(1999)
Electron. Trans. Numer. Anal.
, vol.8
, pp. 138
-
-
Chen, K.1
-
86
-
-
0035537395
-
An analysis of sparse approximate inverse preconditioners for boundary integral equations
-
K. Chen, An analysis of sparse approximate inverse preconditioners for boundary integral equations, SIAM J. Matrix Anal. Appls. 22, 1058 (2001).
-
(2001)
SIAM J. Matrix Anal. Appls.
, vol.22
, pp. 1058
-
-
Chen, K.1
-
87
-
-
0000300094
-
On preconditioned Krylov subspace methods for discrete convection-diffusion problems
-
M. P. Chernesky, On preconditioned Krylov subspace methods for discrete convection-diffusion problems, Numer. Methods Partial Differential Equations 13, 321 (1997).
-
(1997)
Numer. Methods Partial Differential Equations
, vol.13
, pp. 321
-
-
Chernesky, M.P.1
-
88
-
-
0029719756
-
Application of threshold partitioning of sparse matrices to Markov chains
-
Proceedings of the IEEE International Computer Performance and Dependability Symposium, IPDS'96, (IEEE Computer Soc. Press, Los Alamitos, CA)
-
H. Choi and D. B. Szyld, Application of threshold partitioning of sparse matrices to Markov chains, in Proceedings of the IEEE International Computer Performance and Dependability Symposium, IPDS'96, p. 158 (IEEE Computer Soc. Press, Los Alamitos, CA, 1996).
-
(1996)
, pp. 158
-
-
Choi, H.1
Szyld, D.B.2
-
89
-
-
0001261785
-
Fast wavelet iterative solvers applied to the Neumann problem
-
R. Choquet and V. Perrier, Fast wavelet iterative solvers applied to the Neumann problem, Aerospace Sci. Technol. 4, 135 (2000).
-
(2000)
Aerospace Sci. Technol.
, vol.4
, pp. 135
-
-
Choquet, R.1
Perrier, V.2
-
90
-
-
0033678265
-
A priori sparsity patterns for parallel sparse approximate inverse preconditioners
-
E. Chow, A priori sparsity patterns for parallel sparse approximate inverse preconditioners, SIAM J. Sci. Comput. 21, 1804 (2000).
-
(2000)
SIAM J. Sci. Comput.
, vol.21
, pp. 1804
-
-
Chow, E.1
-
91
-
-
0035281285
-
Parallel implementation and performance characteristics of sparse approximate inverse preconditioners with a priori sparsity patterns
-
E. Chow, Parallel implementation and performance characteristics of sparse approximate inverse preconditioners with a priori sparsity patterns, Int. J. High-Perform. Comput. Appl. 15, 56 (2001).
-
(2001)
Int. J. High-Perform. Comput. Appl.
, vol.15
, pp. 56
-
-
Chow, E.1
-
92
-
-
0032083702
-
An object-oriented framework for block preconditioning
-
E. Chow and M. A. Heroux, An object-oriented framework for block preconditioning, ACM Trans. Math. Software 24, 159 (1998).
-
(1998)
ACM Trans. Math. Software
, vol.24
, pp. 159
-
-
Chow, E.1
Heroux, M.A.2
-
93
-
-
0031261348
-
Approximate inverse techniques for block-partitioned matrices
-
E. Chow and Y. Saad, Approximate inverse techniques for block-partitioned matrices, SIAM J. Sci. Comput. 18, 1657 (1997).
-
(1997)
SIAM J. Sci. Comput.
, vol.18
, pp. 1657
-
-
Chow, E.1
Saad, Y.2
-
94
-
-
0031332548
-
Experimental study of ILU preconditioners for indefinite matrices
-
E. Chow and Y. Saad, Experimental study of ILU preconditioners for indefinite matrices, J. Comput. Appl. Math. 86, 387 (1997).
-
(1997)
J. Comput. Appl. Math.
, vol.86
, pp. 387
-
-
Chow, E.1
Saad, Y.2
-
95
-
-
0031251615
-
ILUS: An incomplete ILU preconditioner in sparse skyline format
-
E. Chow and Y. Saad, ILUS: An incomplete ILU preconditioner in sparse skyline format, Int. J. Numer. Methods Fluids 25, 739 (1997).
-
(1997)
Int. J. Numer. Methods Fluids
, vol.25
, pp. 739
-
-
Chow, E.1
Saad, Y.2
-
96
-
-
0001630026
-
Approximate inverse preconditioners via sparse-sparse iterations
-
E. Chow and Y. Saad, Approximate inverse preconditioners via sparse-sparse iterations, SIAM J. Sci. Comput. 19, 995 (1998).
-
(1998)
SIAM J. Sci. Comput.
, vol.19
, pp. 995
-
-
Chow, E.1
Saad, Y.2
-
97
-
-
0033710185
-
Robustness and scalability of algebraic multigrid
-
A. J. Cleary, R. D. Falgout, V. E. Henson, J. J. Jones, T A. Manteuffel, S. F. McCormick, G. N. Miranda, and J. W. Ruge, Robustness and scalability of algebraic multigrid, SIAM J. Sci. Comput. 21, 1886 (2000).
-
(2000)
SIAM J. Sci. Comput.
, vol.21
, pp. 1886
-
-
Cleary, A.J.1
Falgout, R.D.2
Henson, V.E.3
Jones, J.J.4
Manteuffel, T.A.5
McCormick, S.F.6
Miranda, G.N.7
Ruge, J.W.8
-
98
-
-
0002337314
-
Weighted graph based ordering techniques for preconditioned conjugate gradient methods
-
S. S. Clift and W.-P. Tang, Weighted graph based ordering techniques for preconditioned conjugate gradient methods, BIT 35, 30 (1995).
-
(1995)
BIT
, vol.35
, pp. 30
-
-
Clift, S.S.1
Tang, W.-P.2
-
99
-
-
0033297111
-
Wavelet methods for second-order elliptic problems, preconditioning, and adaptivity
-
A. Cohen and R. Masson, Wavelet methods for second-order elliptic problems, preconditioning, and adaptivity, SIAM J. Sci. Comput. 21, 1006 (1999).
-
(1999)
SIAM J. Sci. Comput.
, vol.21
, pp. 1006
-
-
Cohen, A.1
Masson, R.2
-
100
-
-
0001249888
-
Block preconditioning for the conjugate gradient method
-
P. Concus, G. H. Golub, and G. Meurant, Block preconditioning for the conjugate gradient method, SIAM J. Sci. Stat. Comput. 6, 220 (1985).
-
(1985)
SIAM J. Sci. Stat. Comput.
, vol.6
, pp. 220
-
-
Concus, P.1
Golub, G.H.2
Meurant, G.3
-
101
-
-
0002540389
-
A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations
-
edited by J. R. Bunch and D. J, Rose (Academic Press, New York
-
P. Concus, G. H. Golub, and D. P. O'Leary, A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations, in Sparse Matrix Computations, edited by J. R. Bunch and D. J, Rose, p. 309 (Academic Press, New York, 1976).
-
(1976)
Sparse Matrix Computations
, pp. 309
-
-
Concus, P.1
Golub, G.H.2
O'Leary, D.P.3
-
102
-
-
0002457199
-
Approximate inverse preconditioning for sparse linear systems
-
J. D. F. Cosgrove, J. C. Díaz, and A. Griewank, Approximate inverse preconditioning for sparse linear systems, Int. J. Comput. Math. 44, 91 (1992).
-
(1992)
Int. J. Comput. Math.
, vol.44
, pp. 91
-
-
Cosgrove, J.D.F.1
Díaz, J.C.2
Griewank, A.3
-
103
-
-
0001803542
-
Several strategies for reducing the bandwidth of matrices
-
edited by D. J. Rose and R. A. Willoughby (Plenum, New York
-
E. Cuthill, Several strategies for reducing the bandwidth of matrices, in Sparse Matrices and Their Applications, p. 157, edited by D. J. Rose and R. A. Willoughby (Plenum, New York, 1972).
-
(1972)
Sparse Matrices and Their Applications
, vol.157
-
-
Cuthill, E.1
-
104
-
-
0012123163
-
Algebraic multigrid methods and the Schur complement
-
Robust MultiGrid Methods (Kiel 1988) Vieweg, Braunschweig
-
W. Dahmen and L. Elsner, Algebraic multigrid methods and the Schur complement, in Robust MultiGrid Methods (Kiel 1988), Notes in Numerical Fluid Mechanics 23, p. 58 (Vieweg, Braunschweig, 1989).
-
(1989)
Notes in Numerical Fluid Mechanics
, vol.23
, pp. 58
-
-
Dahmen, W.1
Elsner, L.2
-
105
-
-
0034455094
-
The fast multipole method. I. Error analysis and asymptotic complexity
-
E. Darve, The fast multipole method. I. Error analysis and asymptotic complexity, SIAM J. Numer. Anal. 38, 98 (2000).
-
(2000)
SIAM J. Numer. Anal.
, vol.38
, pp. 98
-
-
Darve, E.1
-
106
-
-
0000893843
-
The fast multipole method: Numerical implementation
-
E. Darve, The fast multipole method: Numerical implementation, J. Comput. Phys. 160, 195 (2000).
-
(2000)
J. Comput. Phys.
, vol.160
, pp. 195
-
-
Darve, E.1
-
107
-
-
85190770112
-
-
University of Florida Sparse Matrix Collection, NA Digest, Vol. 92, No. 42, October 16, 1994; NA Digest, Vol. 96, No. 28, July 23, 1996; and NA Digest, Vol. 97, No. 23, June 7, 1997, available at ftp://ftp.cise.ufl.edu/pub/faculty/davis/matrices
-
T. A. Davis, University of Florida Sparse Matrix Collection, NA Digest, Vol. 92, No. 42, October 16, 1994; NA Digest, Vol. 96, No. 28, July 23, 1996; and NA Digest, Vol. 97, No. 23, June 7, 1997, available at http://www.cise.ufl.edu/research/sparse/matrices, ftp://ftp.cise.ufl.edu/pub/faculty/davis/matrices.
-
-
-
Davis, T.A.1
-
108
-
-
0000565358
-
Ordering methods for preconditioned conjugate gradient methods applied to unstructured grid problems
-
E. F. D'Azevedo, P. A. Forsyth, and W.-P. Tang, Ordering methods for preconditioned conjugate gradient methods applied to unstructured grid problems, SIAM J. Matrix Anal. Appl. 13, 944 (1992).
-
(1992)
SIAM J. Matrix Anal. Appl.
, vol.13
, pp. 944
-
-
D'Azevedo, E.F.1
Forsyth, P.A.2
Tang, W.-P.3
-
109
-
-
6044256950
-
Two variants of minimum discarded fill ordering
-
edited by R. Beauwens and P. de Groen Elsevier Science North-Holland
-
E. F. D'Azevedo, P. A. Forsyth, and W.-P. Tang, Two variants of minimum discarded fill ordering, in Iterative Methods in Linear Algebra, edited by R. Beauwens and P. de Groen, p. 603 (Elsevier Science, North-Holland, 1992).
-
(1992)
Iterative Methods in Linear Algebra
, vol.603
-
-
D'Azevedo, E.F.1
Forsyth, P.A.2
Tang, W.-P.3
-
110
-
-
0001677218
-
Black box multigrid
-
J. E. Dendy, Black box multigrid, J. Comput. Phys. 48, 366 (1980).
-
(1980)
J. Comput. Phys.
, vol.48
, pp. 366
-
-
Dendy, J.E.1
-
111
-
-
85190808907
-
Coarse grain preconditioned conjugate gradient solver for large sparse systems
-
Proceedings of the Seventh SIAM Conference on Parallel-Processing for Scientific Computing, edited by J. Lewis (SIAM, Philadelphia, PA
-
E. de Doncker and A. K. Gupta, Coarse grain preconditioned conjugate gradient solver for large sparse systems, in Proceedings of the Seventh SIAM Conference on Parallel-Processing for Scientific Computing, edited by J. Lewis, p. 472 (SIAM, Philadelphia, PA, 1995).
-
(1995)
, vol.472
-
-
de Doncker, E.1
Gupta, A.K.2
-
112
-
-
84966252352
-
Decay rates for inverses of band matrices
-
S. Demko, W. F. Moss, and P. W. Smith, Decay rates for inverses of band matrices, Math. Comput. 43, 491 (1984).
-
(1984)
Math. Comput.
, vol.43
, pp. 491
-
-
Demko, S.1
Moss, W.F.2
Smith, P.W.3
-
113
-
-
0035219561
-
Incomplete multilevel Cholesky factorizations
-
J. C. Díaz and K. Komara, Incomplete multilevel Cholesky factorizations, SIAM J. Matrix Anal. Appl. 22, 895 (2000).
-
(2000)
SIAM J. Matrix Anal. Appl.
, vol.22
, pp. 895
-
-
Díaz, J.C.1
Komara, K.2
-
114
-
-
0000674152
-
On parallelism and convergence of incomplete LU factorizations
-
S. Doi, On parallelism and convergence of incomplete LU factorizations, Appl. Numer. Math. 7, 417 (1991).
-
(1991)
Appl. Numer. Math.
, vol.7
, pp. 417
-
-
Doi, S.1
-
115
-
-
0033283378
-
Ordering strategies and related techniques to overcome the trade-off between parallelism and convergence in incomplete factorizations
-
S. Doi and T. Washio, Ordering strategies and related techniques to overcome the trade-off between parallelism and convergence in incomplete factorizations, Parallel Comput. 25, 1995 (1999).
-
(1999)
Parallel Comput.
, vol.25
, pp. 1995
-
-
Doi, S.1
Washio, T.2
-
116
-
-
0003851784
-
Numerical Linear Algebra for High-Performance Computers
-
SIAM, Philadelphia, PA
-
J. J. Dongarra, I. S. Duff, D. C. Sorensen, and H. A. van der Vorst, Numerical Linear Algebra for High-Performance Computers (SIAM, Philadelphia, PA, 1998).
-
(1998)
-
-
Dongarra, J.J.1
Duff, I.S.2
Sorensen, D.C.3
van der Vorst, H.A.4
-
117
-
-
84967782959
-
On the numerical solution of heat conduction problems in two or three space variables
-
J. Douglas, Jr., and H. H. Rachford, Jr., On the numerical solution of heat conduction problems in two or three space variables, Trans. Am. Math. Soc. 82,421 (1956).
-
(1956)
Trans. Am. Math. Soc.
, vol.82
, pp. 421
-
-
Douglas J., Jr.1
Rachford H.H., Jr.2
-
118
-
-
34249760088
-
Numerical stabilty of GMRES
-
J. Drkošová, A. Greenbaum, M. Rozložnik, and Z. Strakoš, Numerical stabilty of GMRES, BIT 35, 309 (1995).
-
(1995)
BIT
, vol.35
, pp. 309
-
-
Drkošová, J.1
Greenbaum, A.2
Rozložnik, M.3
Strakoš, Z.4
-
119
-
-
0018707156
-
Approximating the inverse of a matrix for use in iterative algorithms on vector processors
-
P. F. Dubois, A. Greenbaum, and G. H. Rodrigue, Approximating the inverse of a matrix for use in iterative algorithms on vector processors, Computing 22, 257 (1979).
-
(1979)
Computing
, vol.22
, pp. 257
-
-
Dubois, P.F.1
Greenbaum, A.2
Rodrigue, G.H.3
-
120
-
-
0002324734
-
Sparsity structure and Gaussian elimination
-
I. S. Duff, A. M. Erisman, C. W. Gear, and J. K. Reid, Sparsity structure and Gaussian elimination, SIGNUM Newsl. 23, 2 (1988).
-
(1988)
SIGNUM Newsl.
, vol.23
, pp. 2
-
-
Duff, I.S.1
Erisman, A.M.2
Gear, C.W.3
Reid, J.K.4
-
121
-
-
0003554095
-
Direct Methods for Sparse Matrices
-
Clarendon, Oxford
-
I. S. Duff, A. M. Erisman, and J. K. Reid, Direct Methods for Sparse Matrices (Clarendon, Oxford, 1986).
-
(1986)
-
-
Duff, I.S.1
Erisman, A.M.2
Reid, J.K.3
-
122
-
-
0003452796
-
The Rutherford-Boeing Sparse Matrix Collection
-
Technical Report RAL-TR-97-031 Rutherford Appleton Laboratory, Chilton UK
-
I. S. Duff, R. G. Grimes, and J. G. Lewis, The Rutherford-Boeing Sparse Matrix Collection, Technical Report RAL-TR-97-031 (Rutherford Appleton Laboratory, Chilton, UK, 1997).
-
(1997)
-
-
Duff, I.S.1
Grimes, R.G.2
Lewis, J.G.3
-
123
-
-
0033242220
-
The design and use of algorithms for permuting large entries to the diagonal of sparse matrices
-
I. S. Duff and J. Koster, The design and use of algorithms for permuting large entries to the diagonal of sparse matrices, SIAM J. Matrix Anal. Appl. 20, 889 (1999).
-
(1999)
SIAM J. Matrix Anal. Appl.
, vol.20
, pp. 889
-
-
Duff, I.S.1
Koster, J.2
-
124
-
-
0035537388
-
On algorithms for permuting large entries to the diagonal of a sparse matrix
-
I. S. Duff and J. Koster, On algorithms for permuting large entries to the diagonal of a sparse matrix, SIAM J. Matrix Anal. Appl. 22, 973 (2001).
-
(2001)
SIAM J. Matrix Anal. Appl.
, vol.22
, pp. 973
-
-
Duff, I.S.1
Koster, J.2
-
125
-
-
0000602242
-
The effect of ordering on preconditioned conjugate gradients
-
I. S. Duff and G. Meurant, The effect of ordering on preconditioned conjugate gradients, BIT 29, 635 (1989).
-
(1989)
BIT
, vol.29
, pp. 635
-
-
Duff, I.S.1
Meurant, G.2
-
126
-
-
0000762041
-
An approximate factorization procedure for solving self-adjoint elliptic difference equations
-
T. Dupont, R. P. Kendall, and H. H. Rachford, Jr., An approximate factorization procedure for solving self-adjoint elliptic difference equations, SIAM J. Numer. Anal. 5, 559 (1968).
-
(1968)
SIAM J. Numer. Anal.
, vol.5
, pp. 559
-
-
Dupont, T.1
Kendall, R.P.2
Rachford H.H., Jr.3
-
127
-
-
0027545264
-
The effect of ordering on preconditioned GMRES algorithm, for solving the compressible Navier-Stokes equations
-
L. C. Dutto, The effect of ordering on preconditioned GMRES algorithm, for solving the compressible Navier-Stokes equations, Int. J. Numer. Methods Eng. 36, 457 (1993).
-
(1993)
Int. J. Numer. Methods Eng.
, vol.36
, pp. 457
-
-
Dutto, L.C.1
-
128
-
-
0000877266
-
Analysis of parallel incomplete point factorizations
-
V. Eijkhout, Analysis of parallel incomplete point factorizations, Linear Algebra Its Appl. 154, 723 (1991).
-
Linear Algebra Its Appl.
, vol.154
-
-
Eijkhout, V.1
-
129
-
-
0003223995
-
Beware of unperturbed modified incomplete factorizations
-
edited by R. Beauwens and P. de Groen Elsevier Science, North-Holland
-
V. Eijkhout, Beware of unperturbed modified incomplete factorizations, in Iterative Methods in Linear Algebra, edited by R. Beauwens and P. de Groen, p. 583 (Elsevier Science, North-Holland, 1992).
-
(1992)
Iterative Methods in Linear Algebra
, vol.583
-
-
Eijkhout, V.1
-
130
-
-
0002705646
-
Efficient implementation of a class of conjugate gradient methods
-
S. Eisenstat, Efficient implementation of a class of conjugate gradient methods, SIAM J. Sci. Stat. Comput. 2, 1 (1981).
-
(1981)
SIAM J. Sci. Stat. Comput.
, vol.2
, pp. 1
-
-
Eisenstat, S.1
-
131
-
-
84966211825
-
A stability analysis of incomplete LU factorizations
-
H. C. Elman, A stability analysis of incomplete LU factorizations, Math. Comput. 47, 191 (1986).
-
(1986)
Math. Comput.
, vol.47
, pp. 191
-
-
Elman, H.C.1
-
132
-
-
0027678586
-
Ordering effects on relaxation methods applied to the discrete one-dimensional convection-diffusion equation
-
H. C. Elman and M. P. Chernesky, Ordering effects on relaxation methods applied to the discrete one-dimensional convection-diffusion equation, SIAM J. Numer. Anal. 30, 1268 (1993).
-
(1993)
SIAM J. Numer. Anal.
, vol.30
, pp. 1268
-
-
Elman, H.C.1
Chernesky, M.P.2
-
133
-
-
0012160938
-
Refined Iterative Methods for Computation of the Solution and the Eigenvalues of Self-Adjoint Boundary Value Problems
-
Birkhäuser Basel/Stuttgart
-
M. Engeli, Th. Ginsburg, H. Rutishauser, and E. Stiefel, Refined Iterative Methods for Computation of the Solution and the Eigenvalues of Self-Adjoint Boundary Value Problems (Birkhäuser, Basel/Stuttgart, 1959).
-
(1959)
-
-
Engeli, M.1
Ginsburg, Th.2
Rutishauser, H.3
Stiefel, E.4
-
134
-
-
0000234821
-
The use of pre-conditioning in iterative methods for solving linear systems with symmetric positive definite matrices
-
D. J. Evans, The use of pre-conditioning in iterative methods for solving linear systems with symmetric positive definite matrices, J. Inst. Math. Its Appl. 4, 295 (1968).
-
(1968)
J. Inst. Math. Its Appl.
, vol.4
, pp. 295
-
-
Evans, D.J.1
-
135
-
-
0026239487
-
A method of finite-element tearing and interconnecting and its parallel solution algorithm
-
C. Farhat and F.-X. Roux, A method of finite-element tearing and interconnecting and its parallel solution algorithm, Int. J. Numer. Methods Eng. 32, 1205 (1991).
-
(1991)
Int. J. Numer. Methods Eng.
, vol.32
, pp. 1205
-
-
Farhat, C.1
Roux, F.-X.2
-
136
-
-
0028429575
-
Optimal convergence properties of the FETI domain decomposition method
-
C. Farhat, J. Mandel, and F.-X. Roux, Optimal convergence properties of the FETI domain decomposition method, Comput. Methods Appl. Mech. Eng. 115, 365 (1994).
-
(1994)
Comput. Methods Appl. Mech. Eng.
, vol.115
, pp. 365
-
-
Farhat, C.1
Mandel, J.2
Roux, F.-X.3
-
137
-
-
0032022379
-
The two-level FETI method for static and dynamic plate problems. Part I: An optimal iterative solver for biharmonic systems
-
C. Farhat and J. Mandel, The two-level FETI method for static and dynamic plate problems. Part I: An optimal iterative solver for biharmonic systems, Comput. Methods Appl. Mech. Eng. 155, 129 (1998).
-
(1998)
Comput. Methods Appl. Mech. Eng.
, vol.155
, pp. 129
-
-
Farhat, C.1
Mandel, J.2
-
138
-
-
50549189861
-
A relaxation method for solving elliptic difference equations
-
R. P. Fedorenko, A relaxation method for solving elliptic difference equations, USSR Comput. Math. Math. Phys. 1, 1092 (1961).
-
(1961)
USSR Comput. Math. Math. Phys.
, vol.1
, pp. 1092
-
-
Fedorenko, R.P.1
-
139
-
-
0001038302
-
The speed of convergence of one iterative process
-
R. P. Fedorenko, The speed of convergence of one iterative process, USSR Comput. Math. Math. Phys. 4, 227 (1964).
-
(1964)
USSR Comput. Math. Math. Phys.
, vol.4
, pp. 227
-
-
Fedorenko, R.P.1
-
140
-
-
0003705273
-
An Efficient Parallel Preconditioner for the Conjugate Gradient Algorithm
-
Hitachi Dublin Laboratory Technical Report HDL-TR-97-175 Dublin, Ireland
-
M. R. Field, An Efficient Parallel Preconditioner for the Conjugate Gradient Algorithm, Hitachi Dublin Laboratory Technical Report HDL-TR-97-175 (Dublin, Ireland, 1997).
-
(1997)
-
-
Field, M.R.1
-
141
-
-
0003423573
-
Improving the Performance of Factorised Sparse Approximate Inverse Preconditioner
-
Hitachi Dublin Laboratory Technical Report HDL-TR-98-199 Dublin, Ireland
-
M. R. Field, Improving the Performance of Factorised Sparse Approximate Inverse Preconditioner, Hitachi Dublin Laboratory Technical Report HDL-TR-98-199 (Dublin, Ireland, 1998).
-
(1998)
-
-
Field, M.R.1
-
142
-
-
0003808436
-
Polynomial Based Iteration Methods for Symmetric Linear Systems
-
Wiley-Teubner, Chichester
-
B. Fischer, Polynomial Based Iteration Methods for Symmetric Linear Systems (Wiley-Teubner, Chichester, 1996).
-
(1996)
-
-
Fischer, B.1
-
143
-
-
0002308279
-
Conjugate gradient methods for indefinite systems
-
edited by G. A. Watson 73 Lecture Notes in Mathematics No. 506 Springer, Berlin
-
R. Fletcher, Conjugate gradient methods for indefinite systems, in Numerical Analysis Dundee 1975, edited by G. A. Watson, p. 73, Lecture Notes in Mathematics No. 506 (Springer, Berlin, 1976).
-
(1976)
Numerical Analysis Dundee 1975
-
-
Fletcher, R.1
-
144
-
-
2942551017
-
Notes on the solution of algebraic linear simultaneous equations
-
L. Fox L, H. D. Huskey, and J. H. Wilkinson, Notes on the solution of algebraic linear simultaneous equations, Q. J. Mech. Appl. Math. 1, 149 (1948).
-
(1948)
Q. J. Mech. Appl. Math.
, vol.1
, pp. 149
-
-
Fox, L.1
Huskey, L.H.D.2
Wilkinson, J.H.3
-
145
-
-
0012159377
-
Fast Approximate Inversion of Large Sparse Linear Systems
-
Math. Report 7 (Lakehead University, Thunder Bay, Ontario,)
-
P. O. Frederickson, Fast Approximate Inversion of Large Sparse Linear Systems, Math. Report 7 (Lakehead University, Thunder Bay, Ontario, 1975).
-
(1975)
-
-
Frederickson, P.O.1
-
146
-
-
0001031880
-
A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems
-
R. Freund, A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems, SIAM J. Sci. Comput. 14, 470 (1993).
-
(1993)
SIAM J. Sci. Comput.
, vol.14
, pp. 470
-
-
Freund, R.1
-
147
-
-
84968452648
-
Iterative solution of linear systems
-
R. Freund, G. H. Golub, and N. M. Nachtigal, Iterative solution of linear systems, Acta Numer. 1, 57 (1991).
-
(1991)
Acta Numer.
, vol.1
, pp. 57
-
-
Freund, R.1
Golub, G.H.2
Nachtigal, N.M.3
-
148
-
-
25444452938
-
QMR: A quasi-minimal residual method for non-Hermitian linear systems
-
R. Freund and N. M. Nachtigal, QMR: A quasi-minimal residual method for non-Hermitian linear systems, Numer. Math. 60, 315 (1991).
-
(1991)
Numer. Math.
, vol.60
, pp. 315
-
-
Freund, R.1
Nachtigal, N.M.2
-
149
-
-
0000264382
-
Nested dissection of a regular finite element mesh
-
A. George, Nested dissection of a regular finite element mesh, SIAM J. Numer. Anal. 10, 345 (1973).
-
(1973)
SIAM J. Numer. Anal.
, vol.10
, pp. 345
-
-
George, A.1
-
150
-
-
0003645035
-
Computer Solution of Large Sparse Positive Definite Systems
-
(Prentice-Hall, Englewood Cliffs, NJ)
-
A. George and J. W. Liu, Computer Solution of Large Sparse Positive Definite Systems (Prentice-Hall, Englewood Cliffs, NJ, 1981).
-
(1981)
-
-
George, A.1
Liu, J.W.2
-
151
-
-
0024630993
-
The evolution of the minimum degree algorithm
-
A. George and J. W. Liu, The evolution of the minimum degree algorithm, SIAM Rev. 31, 1 (1989).
-
(1989)
SIAM Rev.
, vol.31
, pp. 1
-
-
George, A.1
Liu, J.W.2
-
152
-
-
0016939622
-
An algorithm for reducing the bandwidth and profile of a sparse matrix
-
N. E. Gibbs, W. G. Poole, Jr., and R K. Stockmeyer, An algorithm for reducing the bandwidth and profile of a sparse matrix, SIAM J. Numer. Anal. 13, 236 (1976).
-
(1976)
SIAM J. Numer. Anal.
, vol.13
, pp. 236
-
-
Gibbs, N.E.1
Poole W.G., Jr.2
Stockmeyer, R.K.3
-
153
-
-
21344476775
-
Predicting structure in sparse matrix computations
-
J. R. Gilbert, Predicting structure in sparse matrix computations, SIAM J. Matrix Anal. Appl. 15, 62 (1994).
-
(1994)
SIAM J. Matrix Anal. Appl.
, vol.15
, pp. 62
-
-
Gilbert, J.R.1
-
155
-
-
0024631560
-
Some history of the conjugate gradient and Lanczos methods: 1948-1976
-
G. H. Golub and D. P. O'Leary, Some history of the conjugate gradient and Lanczos methods: 1948-1976, SIAM Rev. 31, 50 (1989).
-
(1989)
SIAM Rev.
, vol.31
, pp. 50
-
-
Golub, G.H.1
O'Leary, D.P.2
-
157
-
-
0033293064
-
Inexact preconditioned conjugate-gradient method with inner-outer iteration
-
G. H. Golub and Q. Ye, Inexact preconditioned conjugate-gradient method with inner-outer iteration, SIAM J. Sci. Comput. 21, 1305 (1999).
-
(1999)
SIAM J. Sci. Comput.
, vol.21
, pp. 1305
-
-
Golub, G.H.1
Ye, Q.2
-
158
-
-
0000478318
-
Sparse approximate-inverse preconditioners using norm-minimization techniques
-
N. I. M. Gould and J. A. Scott, Sparse approximate-inverse preconditioners using norm-minimization techniques, SIAM J. Sci. Comput. 19, 605 (1998).
-
(1998)
SIAM J. Sci. Comput.
, vol.19
, pp. 605
-
-
Gould, N.I.M.1
Scott, J.A.2
-
159
-
-
0021451206
-
Analysis of a multigrid method as an iterative method for solving linear systems
-
A. Greenbaum, Analysis of a multigrid method as an iterative method for solving linear systems, SIAM J. Numer. Anal. 21, 473 (1984).
-
(1984)
SIAM J. Numer. Anal.
, vol.21
, pp. 473
-
-
Greenbaum, A.1
-
160
-
-
0003470761
-
Iterative Methods for Solving Linear Systems
-
(SIAM, Philadelphia, PA)
-
A. Greenbaum, Iterative Methods for Solving Linear Systems (SIAM, Philadelphia, PA, 1997).
-
(1997)
-
-
Greenbaum, A.1
-
161
-
-
0041049302
-
Any nonincreasing convergence curve is possible for GMRES
-
A. Greenbaum, V. Pák, and Z. Strakoš, Any nonincreasing convergence curve is possible for GMRES, SIAM J. Matrix Anal. Appl. 17, 465 (1996).
-
(1996)
SIAM J. Matrix Anal. Appl.
, vol.17
, pp. 465
-
-
Greenbaum, A.1
Pák, V.2
Strakoš, Z.3
-
162
-
-
0000002780
-
Predicting the behavior of finite precision Lanczos and conjugate gradient computations
-
A. Greenbaum and Z. Strakoš, Predicting the behavior of finite precision Lanczos and conjugate gradient computations, SIAM J. Matrix Anal. Appl. 13, 121 (1992).
-
(1992)
SIAM J. Matrix Anal. Appl.
, vol.13
, pp. 121
-
-
Greenbaum, A.1
Strakoš, Z.2
-
163
-
-
0031129197
-
Parallel preconditioning with sparse approximate inverses
-
M. Grote and T. Huckle, Parallel preconditioning with sparse approximate inverses, SIAM J. Sci. Comput. 18, 838 (1997).
-
(1997)
SIAM J. Sci. Comput.
, vol.18
, pp. 838
-
-
Grote, M.1
Huckle, T.2
-
164
-
-
0003039594
-
A class of first order factorization methods
-
I. Gustafsson, A class of first order factorization methods, BIT 18, 142 (1978).
-
(1978)
BIT
, vol.18
, pp. 142
-
-
Gustafsson, I.1
-
165
-
-
0032179234
-
Parallel incomplete Cholesky preconditioners based on the nonoverlapping data distribution
-
G. Haase, Parallel incomplete Cholesky preconditioners based on the nonoverlapping data distribution, Parallel Comput. 24, 1685 (1998).
-
(1998)
Parallel Comput.
, vol.24
, pp. 1685
-
-
Haase, G.1
-
166
-
-
0003815501
-
Multi-Grid Methods and Applications
-
(Springer-Verlag, Berlin)
-
W. Hackbusch, Multi-Grid Methods and Applications (Springer-Verlag, Berlin, 1985).
-
(1985)
-
-
Hackbusch, W.1
-
167
-
-
0003826505
-
Iterative Solution of Large Sparse Systems of Equations
-
(Springer-Verlag, New York)
-
W. Hackbusch, Iterative Solution of Large Sparse Systems of Equations (Springer-Verlag, New York, 1994).
-
(1994)
-
-
Hackbusch, W.1
-
168
-
-
0004207233
-
Applied Iterative Methods
-
(Academic Press, New York)
-
A. L. Hageman and D. M. Young, Applied Iterative Methods (Academic Press, New York, 1981).
-
(1981)
-
-
Hageman, A.L.1
Young, D.M.2
-
169
-
-
0035246496
-
Efficient ILU preconditioning and inexact-Newton-GMRES to solve the 2D steady shallow water equations
-
M. Heniche, Y. Secretan, and M. Leclerc, Efficient ILU preconditioning and inexact-Newton-GMRES to solve the 2D steady shallow water equations, Commun. Numer. Methods Eng. 17, 69 (2001).
-
(2001)
Commun. Numer. Methods Eng.
, vol.17
, pp. 69
-
-
Heniche, M.1
Secretan, Y.2
Leclerc, M.3
-
170
-
-
0036532956
-
BoomerAMG: A parallel algebraic multigrid solver and preconditioner
-
V. E. Henson and U. M. Yang, BoomerAMG: A parallel algebraic multigrid solver and preconditioner, Appl. Numer. Math, 41, 155 (2002).
-
(2002)
Appl. Numer. Math,
, vol.41
, pp. 155
-
-
Henson, V.E.1
Yang, U.M.2
-
171
-
-
0000135303
-
Methods of conjugate gradients for solving linear systems
-
M. R. Hestenes and E. L. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Natl. Bur. Stand. 49, 409 (1952).
-
(1952)
J. Res. Natl. Bur. Stand.
, vol.49
, pp. 409
-
-
Hestenes, M.R.1
Stiefel, E.L.2
-
172
-
-
0031167176
-
Robust preconditioners for linear elasticity FEM analyses
-
I, Hladík, M. B. Reed, and G. Swoboda, Robust preconditioners for linear elasticity FEM analyses, Int. J. Numer. Methods Eng. 40, 2109 (1997).
-
(1997)
Int. J. Numer. Methods Eng.
, vol.40
, pp. 2109
-
-
Hladík, I.1
Reed, M.B.2
Swoboda, G.3
-
173
-
-
0003757202
-
The Theory of Matrices in Numerical Analysis
-
(Blaisdell, New York)
-
A. S. Householder, The Theory of Matrices in Numerical Analysis (Blaisdell, New York, 1964).
-
(1964)
-
-
Householder, A.S.1
-
174
-
-
0033149565
-
Approximate sparsity patterns for the inverse of a matrix and preconditioning
-
T. Huckle, Approximate sparsity patterns for the inverse of a matrix and preconditioning, Appl. Numer. Math. 30, 291 (1999).
-
(1999)
Appl. Numer. Math.
, vol.30
, pp. 291
-
-
Huckle, T.1
-
175
-
-
0012195489
-
Factorized sparse approximate inverses for preconditioning and smoothing
-
T. Huckle, Factorized sparse approximate inverses for preconditioning and smoothing, Selčuk J, Appl. Math, 1, 63 (2000).
-
(2000)
Selčuk J, Appl. Math,
, vol.1
, pp. 63
-
-
Huckle, T.1
-
176
-
-
85190777769
-
Factorized sparse approximate inverses for preconditioning
-
Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA 2001), (CSREA Press, Las Vegas, Nevada)
-
T. Huckle, Factorized sparse approximate inverses for preconditioning, in Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA 2001), (CSREA Press, Las Vegas, Nevada, 2001).
-
(2001)
-
-
Huckle, T.1
-
177
-
-
85190763768
-
New Sequential and Scalable Parallel Algorithms for Incomplete Factor Preconditioning
-
Ph.D, thesis (Dep. Computer Science, Old Dominion Univ., Norfolk, VA)
-
D. Hysom, New Sequential and Scalable Parallel Algorithms for Incomplete Factor Preconditioning, Ph.D, thesis (Dep. Computer Science, Old Dominion Univ., Norfolk, VA, 2001).
-
(2001)
-
-
Hysom, D.1
-
178
-
-
0035678671
-
A scalable parallel algorithm for incomplete factor preconditioning
-
D. Hysom and A. Pothen, A scalable parallel algorithm for incomplete factor preconditioning, SIAM J. Sci. Comput. 22, 2194 (2001).
-
(2001)
SIAM J. Sci. Comput.
, vol.22
, pp. 2194
-
-
Hysom, D.1
Pothen, A.2
-
179
-
-
0003768771
-
Iterative Incomplete Factorization Methods
-
(World Scientific, Singapore)
-
V. P. Il'in, Iterative Incomplete Factorization Methods (World Scientific, Singapore, 1992).
-
(1992)
-
-
Il'in, V.P.1
-
180
-
-
0000237258
-
Über eine neue Aufiösungsart der bei der Methode der kleinsten Quadrate vorkornmenden linearen Gleichungen
-
C. G. J. Jacobi, Über eine neue Aufiösungsart der bei der Methode der kleinsten Quadrate vorkornmenden linearen Gleichungen, Astron. Nachrichten 22, 297 (1845).
-
(1845)
Astron. Nachrichten
, vol.22
, pp. 297
-
-
Jacobi, C.G.J.1
-
181
-
-
0000051186
-
Polynomial preconditioning for conjugate gradient calculations
-
O. G. Johnson, C. A. Micchelli, and G. Paul, Polynomial preconditioning for conjugate gradient calculations, SIAM J. Numer. Anal. 20, 362 (1983).
-
(1983)
SIAM J. Numer. Anal.
, vol.20
, pp. 362
-
-
Johnson, O.G.1
Micchelli, C.A.2
Paul, G.3
-
182
-
-
0028434026
-
Scalable iterative solution of sparse linear systems
-
M. T. Jones and P. E. Plassmann, Scalable iterative solution of sparse linear systems, Parallel Comput. 20, 753 (1994).
-
(1994)
Parallel Comput.
, vol.20
, pp. 753
-
-
Jones, M.T.1
Plassmann, P.E.2
-
184
-
-
0012160522
-
Algorithm 740: Fortran subroutines to compute improved incomplete Cholesky factorizations
-
M. T. Jones and P. E. Plassmann, Algorithm 740: Fortran subroutines to compute improved incomplete Cholesky factorizations, ACM Trans. Math. Software 21, 18 (1995).
-
(1995)
ACM Trans. Math. Software
, vol.21
, pp. 18
-
-
Jones, M.T.1
Plassmann, P.E.2
-
185
-
-
84985376638
-
New convergence results and preconditioning strategies for the conjugate gradient method
-
I. E. Kaporin, New convergence results and preconditioning strategies for the conjugate gradient method, Numer. Linear Algebra Appl. 1, 179 (1994).
-
(1994)
Numer. Linear Algebra Appl.
, vol.1
, pp. 179
-
-
Kaporin, I.E.1
-
187
-
-
0036109254
-
A parallel block overlap preconditioning with inexact submatrix inversion for linear elasticity problems
-
I. E. Kaporin and I. N. Konshin, A parallel block overlap preconditioning with inexact submatrix inversion for linear elasticity problems, Numer. Linear Algebra Appl. 9, 141 (2002).
-
(2002)
Numer. Linear Algebra Appl.
, vol.9
, pp. 141
-
-
Kaporin, I.E.1
Konshin, I.N.2
-
188
-
-
0032131147
-
A fast and high quality multilevel scheme for partitioning irregular graphs
-
G. Karypis and V. Kumar, A fast and high quality multilevel scheme for partitioning irregular graphs, SIAM J. Sci. Comput. 20, 359 (1998).
-
(1998)
SIAM J. Sci. Comput.
, vol.20
, pp. 359
-
-
Karypis, G.1
Kumar, V.2
-
189
-
-
0012123164
-
Parallel Threshold-Based ILU Factorization
-
Technical Report 061 (Dep. Computer Science/Army HPC Research Center, Univ. Minnesota, Minneapolis)
-
G. Karypis and V. Kumar, Parallel Threshold-Based ILU Factorization, Technical Report 061 (Dep. Computer Science/Army HPC Research Center, Univ. Minnesota, Minneapolis, 1998).
-
(1998)
-
-
Karypis, G.1
Kumar, V.2
-
190
-
-
0002497330
-
The incomplete Cholesky conjugate gradient method for the iterative solution of systems of linear equations
-
D. S. Kershaw, The incomplete Cholesky conjugate gradient method for the iterative solution of systems of linear equations, J. Comput. Phys. 26, 43 (1978).
-
(1978)
J. Comput. Phys.
, vol.26
, pp. 43
-
-
Kershaw, D.S.1
-
191
-
-
0442281595
-
A robust AINV-type method for constructing sparse approximate inverse preconditioners in factored form
-
S. A. Kharchenko, L. Yu. Kolotilina, A. A. Nikishin, and A. Yu. Yeremin, A robust AINV-type method for constructing sparse approximate inverse preconditioners in factored form, Numer. Linear Algebra Appl. 8, 165 (2001).
-
(2001)
Numer. Linear Algebra Appl.
, vol.8
, pp. 165
-
-
Kharchenko, S.A.1
Kolotilina, L.Yu.2
Nikishin, A.A.3
Yeremin, A.Yu.4
-
192
-
-
0000522446
-
Preconditioned eigensolvers-an oxymoron?
-
A. W. Knyazev, Preconditioned eigensolvers-an oxymoron? Electron. Trans. Numer. Anal. 7, 104 (1998).
-
(1998)
Electron. Trans. Numer. Anal.
, vol.7
, pp. 104
-
-
Knyazev, A.W.1
-
193
-
-
0000950308
-
Explicit preconditioning of systems of linear algebraic equations with dense matrices
-
L. Yu. Kolotilina, Explicit preconditioning of systems of linear algebraic equations with dense matrices, J. Sov. Math. 43, 2566 (1988).
-
(1988)
J. Sov. Math.
, vol.43
, pp. 2566
-
-
Kolotilina, L.Yu.1
-
194
-
-
0033269772
-
Factorized sparse approximate inverse preconditionings. IV: Simple approaches to rising efficiency
-
L. Yu. Kolotilina, A. A. Nikishin, and A. Yu, Yeremin, Factorized sparse approximate inverse preconditionings. IV: Simple approaches to rising efficiency, Numer. Linear Algebra Appl. 6, 515 (1999).
-
(1999)
Numer. Linear Algebra Appl.
, vol.6
, pp. 515
-
-
Kolotilina, L.Yu.1
Nikishin, A.A.2
Yeremin A.Yu3
-
195
-
-
0000747319
-
On a family of two-level preconditionings of the incomplete block factorization type
-
L. Yu. Kolotilina and A. Yu. Yeremin, On a family of two-level preconditionings of the incomplete block factorization type, Sov. J. Numer. Anal. Math. Model. 1, 293 (1986).
-
(1986)
Sov. J. Numer. Anal. Math. Model.
, vol.1
, pp. 293
-
-
Kolotilina, L.Yu.1
Yeremin, A.Yu.2
-
196
-
-
21144474663
-
Factorized sparse approximate inverse preconditioning. I. Theory
-
L. Yu. Kolotilina and A. Yu. Yeremin, Factorized sparse approximate inverse preconditioning. I. Theory, SIAM J. Matrix Anal. Appl. 14, 45 (1993).
-
(1993)
SIAM J. Matrix Anal. Appl.
, vol.14
, pp. 45
-
-
Kolotilina, L.Yu.1
Yeremin, A.Yu.2
-
197
-
-
0000812399
-
Factorized sparse approximate inverse preconditioning. II: Solution of 3D FE systems on massively parallel computers
-
L. Yu. Kolotilina and A. Yu. Yeremin, Factorized sparse approximate inverse preconditioning. II: Solution of 3D FE systems on massively parallel computers, Int. J. High Speed Comput. 7, 191 (1995).
-
(1995)
Int. J. High Speed Comput.
, vol.7
, pp. 191
-
-
Kolotilina, L.Yu.1
Yeremin, A.Yu.2
-
198
-
-
17344378097
-
Parallel algebraic multigrid based on subdomain blocking
-
A. Krechen and K. Stüben, Parallel algebraic multigrid based on subdomain blocking, Parallel Comput. 27, 1009 (2001).
-
(2001)
Parallel Comput.
, vol.27
, pp. 1009
-
-
Krechen, A.1
Stüben, K.2
-
199
-
-
0002814189
-
Solutions of systems of linear equations by minimized iterations
-
C. Lanczos, Solutions of systems of linear equations by minimized iterations, J. Res. Natl. Bur. Stand. 49, 33 (1952).
-
(1952)
J. Res. Natl. Bur. Stand.
, vol.49
, pp. 33
-
-
Lanczos, C.1
-
200
-
-
0020178023
-
Unconditionally stable diffusion-synthetic acceleration methods for the slab geometry discrete ordinates equations. Part I: Theory
-
E. W. Larsen, Unconditionally stable diffusion-synthetic acceleration methods for the slab geometry discrete ordinates equations. Part I: Theory, Nucl. Sci. Eng. 82, 47 (1982).
-
(1982)
Nucl. Sci. Eng.
, vol.82
, pp. 47
-
-
Larsen, E.W.1
-
201
-
-
0012163644
-
Ordering techniques for two- and three-dimensional convection-dominated elliptic boundary value problems
-
S. Le Borne, Ordering techniques for two- and three-dimensional convection-dominated elliptic boundary value problems, Computing 64, 123 (2000).
-
(2000)
Computing
, vol.64
, pp. 123
-
-
Le Borne, S.1
-
202
-
-
0012196501
-
Krylov Methods for the Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations
-
Ph.D. thesis and Technical Report UIUCDS-R-93-1814 (Dep. Computer Science, Univ. Illinois at Urbana-Champaign,)
-
S. L. Lee, Krylov Methods for the Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, Ph.D. thesis and Technical Report UIUCDS-R-93-1814 (Dep. Computer Science, Univ. Illinois at Urbana-Champaign, 1993).
-
(1993)
-
-
Lee, S.L.1
-
203
-
-
0012162477
-
pARMS: A Parallel Version of the Algebraic Recursive Multilevel Solver
-
Technical Report UMSI-2001-100 (Minnesota Supercomputer Institute, Univ. Minnesota, Minneapolis,)
-
N. Li, Y. Saad, and M. Sosonkina, pARMS: A Parallel Version of the Algebraic Recursive Multilevel Solver, Technical Report UMSI-2001-100 (Minnesota Supercomputer Institute, Univ. Minnesota, Minneapolis, 2001).
-
(2001)
-
-
Li, N.1
Saad, Y.2
Sosonkina, M.3
-
204
-
-
0033294627
-
Incomplete Cholesky factorizations with limited memory
-
C.-J. Lin and J. J. Moré, Incomplete Cholesky factorizations with limited memory, SIAM J. Sci. Comput. 21, 24 (1999).
-
(1999)
SIAM J. Sci. Comput.
, vol.21
, pp. 24
-
-
Lin, C.-J.1
Moré, J.J.2
-
205
-
-
0042185149
-
An incomplete Cholesky factorization for dense symmetric positive definite matrices
-
C.-J. Lin and R. Saigal, An incomplete Cholesky factorization for dense symmetric positive definite matrices, BIT 40, 536 (2000).
-
(2000)
BIT
, vol.40
, pp. 536
-
-
Lin, C.-J.1
Saigal, R.2
-
206
-
-
0000843755
-
Generalized nested dissection
-
R. J. Lipton, D. J. Rose, and R. E. Tarjan, Generalized nested dissection, SIAM J. Numer. Anal. 16, 346 (1979).
-
(1979)
SIAM J. Numer. Anal.
, vol.16
, pp. 346
-
-
Lipton, R.J.1
Rose, D.J.2
Tarjan, R.E.3
-
207
-
-
0022077450
-
Modification of the minimum degree algorithm by multiple elimination
-
J. W. H. Liu, Modification of the minimum degree algorithm by multiple elimination, ACM Trans. Math. Software 11, 141 (1985).
-
(1985)
ACM Trans. Math. Software
, vol.11
, pp. 141
-
-
Liu, J.W.H.1
-
208
-
-
21144482411
-
On finding supernodes for sparse matrix computations
-
J. W. H. Liu, E. G. Ng, and B. W. Peyton, On finding supernodes for sparse matrix computations, SIAM J. Matrix Anal. Appl. 14, 242 (1993).
-
(1993)
SIAM J. Matrix Anal. Appl.
, vol.14
, pp. 242
-
-
Liu, J.W.H.1
Ng, E.G.2
Peyton, B.W.3
-
209
-
-
0035916190
-
Incomplete factorization based preconditionings, for solving the Helmholtz equation
-
M. Magolu monga Made, Incomplete factorization based preconditionings, for solving the Helmholtz equation, Int. J. Numer. Methods Eng. 50, 1077 (2001).
-
(2001)
Int. J. Numer. Methods Eng.
, vol.50
, pp. 1077
-
-
Magolu Monga Made, M.1
-
210
-
-
0034314510
-
Preconditioning of discrete Helmholtz operators perturbed by a diagonal complex matrix
-
M. Magolu monga Made, R. Beauwens, and G. Warzée, Preconditioning of discrete Helmholtz operators perturbed by a diagonal complex matrix, Commun. Numer. Methods Eng. 16, 801 (2000).
-
(2000)
Commun. Numer. Methods Eng.
, vol.16
, pp. 801
-
-
Magolu monga Made, M.1
Beauwens, R.2
Warzée, G.3
-
211
-
-
0043190404
-
Experimental comparison of three-dimensional point and line modified incomplete factorization
-
M. Magolu monga Made and B. Polman, Experimental comparison of three-dimensional point and line modified incomplete factorization, Numer. Algorithms 23, 51 (2000).
-
(2000)
Numer. Algorithms
, vol.23
, pp. 51
-
-
Magolu monga Made, M.1
Polman, B.2
-
212
-
-
0035400544
-
Parallel incomplete factorizations with pseudooverlapping subdomains
-
M. Magolu monga Made and H. A. van der Vorst, Parallel incomplete factorizations with pseudooverlapping subdomains, Parallel Comput. 27, 989 (2001).
-
(2001)
Parallel Comput.
, vol.27
, pp. 989
-
-
Magolu monga Made, M.1
van der Vorst, H.A.2
-
213
-
-
84966241510
-
An incomplete factorization technique for positive definite linear systems
-
T. A. Manteuffel, An incomplete factorization technique for positive definite linear systems, Math. Comput. 34, 473 (1980).
-
(1980)
Math. Comput.
, vol.34
, pp. 473
-
-
Manteuffel, T.A.1
-
214
-
-
0020179977
-
Unconditionally stable diffusion-synthetic acceleration methods for the slab geometry discrete ordinates equations. Part II: Numerical results
-
D. R. McCoy and E. W. Larsen, Unconditionally stable diffusion-synthetic acceleration methods for the slab geometry discrete ordinates equations. Part II: Numerical results, Nucl. Sci. Eng. 82, 64 (1982).
-
(1982)
Nucl. Sci. Eng.
, vol.82
, pp. 64
-
-
McCoy, D.R.1
Larsen, E.W.2
-
215
-
-
84966225158
-
An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix
-
J. A. Meijerink and H. A. van der Vorst, An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix, Math. Comput. 31, 148 (1977).
-
(1977)
Math. Comput.
, vol.31
, pp. 148
-
-
Meijerink, J.A.1
van der Vorst, H.A.2
-
216
-
-
0000809242
-
A review of the inverse of symmetric tridiagonal and block tridiagonal matrices
-
G. A. Meurant, A review of the inverse of symmetric tridiagonal and block tridiagonal matrices, SIAM J. Matrix Anal. Appl. 13, 707 (1992).
-
(1992)
SIAM J. Matrix Anal. Appl.
, vol.13
, pp. 707
-
-
Meurant, G.A.1
-
217
-
-
0003733592
-
Computer Solution of Large Linear Systems, Studies in Mathematics and Its Applications
-
(North-Holland, Amsterdam,)
-
G. A. Meurant, Computer Solution of Large Linear Systems, Studies in Mathematics and Its Applications, Vol. 28 (North-Holland, Amsterdam, 1999).
-
(1999)
, vol.28
-
-
Meurant, G.A.1
-
218
-
-
0036253723
-
A multilevel AINV preconditioner
-
G. A. Meurant, A multilevel AINV preconditioner, Numer. Algorithms 29,107 (2002).
-
(2002)
Numer. Algorithms
, vol.29
, pp. 107
-
-
Meurant, G.A.1
-
219
-
-
0001916874
-
Numerical experiments with algebraic multilevel preconditioners
-
G. A. Meurant, Numerical experiments with algebraic multilevel preconditioners, Electron. Trans. Numer. Anal. 12, 1 (2001).
-
(2001)
Electron. Trans. Numer. Anal.
, vol.12
, pp. 1
-
-
Meurant, G.A.1
-
220
-
-
0035452107
-
Parallel approximate factorization method for solving discrete elliptic equations
-
O. Yu. Milyukova, Parallel approximate factorization method for solving discrete elliptic equations, Parallel Comput. 27, 1365 (2001).
-
(2001)
Parallel Comput.
, vol.27
, pp. 1365
-
-
Milyukova, O.Yu.1
-
221
-
-
0034321493
-
Preconditioning eigenvalues and some comparison of solvers
-
R. B. Morgan, Preconditioning eigenvalues and some comparison of solvers, J. Comput. Appl. Math. 123, 101 (2000).
-
(2000)
J. Comput. Appl. Math.
, vol.123
, pp. 101
-
-
Morgan, R.B.1
-
222
-
-
0000109908
-
Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion
-
V. A. Mousseau, D. A. Knoll, and W. J. Rider, Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion, J. Comput. Phys. 160, 743 (2000).
-
(2000)
J. Comput. Phys.
, vol.160
, pp. 743
-
-
Mousseau, V.A.1
Knoll, D.A.2
Rider, W.J.3
-
223
-
-
0034497397
-
A note on preconditioning for indefinite linear systems
-
M. F. Murphy, G. H. Golub, and A. J. Wathen, A note on preconditioning for indefinite linear systems, SIAM J. Sci. Comput. 21, 1969 (2000).
-
(2000)
SIAM J. Sci. Comput.
, vol.21
, pp. 1969
-
-
Murphy, M.F.1
Golub, G.H.2
Wathen, A.J.3
-
224
-
-
0011262213
-
-
Ed., (Addison-Wesley, Reading, MA,)
-
S. G. Nash, Ed., A History of Scientific Computing (Addison-Wesley, Reading, MA, 1990).
-
(1990)
A History of Scientific Computing
-
-
Nash, S.G.1
-
225
-
-
85190780893
-
-
National Institute of Standards, Matrix Market, available online at
-
National Institute of Standards, Matrix Market, available online at http://math.nist.gov/MatrixMarket.
-
-
-
-
226
-
-
0000632584
-
A blocked incomplete Cholesky preconditioner for hierarchical-memory computers
-
edited by D. R. Kincaid and A. C. Elster, IMACS Series in Computational and Applied Mathematics, (IMACS, New Brunswick, NJ,)
-
E. Ng, B. W. Peyton, and P. Raghavan, A blocked incomplete Cholesky preconditioner for hierarchical-memory computers, in Iterative Methods in Scientific Computation IV, edited by D. R. Kincaid and A. C. Elster, IMACS Series in Computational and Applied Mathematics, Vol. 5, 211 (IMACS, New Brunswick, NJ, 1999).
-
(1999)
Iterative Methods in Scientific Computation IV
, vol.5
, pp. 211
-
-
Ng, E.1
Peyton, B.W.2
Raghavan, P.3
-
227
-
-
0032344210
-
Using approximate inverses in algebraic multilevel methods
-
Y. Notay, Using approximate inverses in algebraic multilevel methods, Numer. Math. 80, 397 (1998).
-
(1998)
Numer. Math.
, vol.80
, pp. 397
-
-
Notay, Y.1
-
228
-
-
0033207377
-
A multilevel block incomplete factorization preconditioning
-
Y. Notay, A multilevel block incomplete factorization preconditioning, Appl. Numer. Math. 31, 209 (1999).
-
(1999)
Appl. Numer. Math.
, vol.31
, pp. 209
-
-
Notay, Y.1
-
229
-
-
0034511247
-
Optimal order preconditioning of finite difference matrices
-
Y. Notay, Optimal order preconditioning of finite difference matrices, SIAM J. Sci. Comput. 21, 1991 (2000).
-
(2000)
SIAM J. Sci. Comput.
, vol.21
, pp. 1991
-
-
Notay, Y.1
-
230
-
-
0034880095
-
Flexible conjugate gradient
-
Y. Notay, Flexible conjugate gradient, SIAM J. Sci. Comput. 22, 1444 (2000).
-
(2000)
SIAM J. Sci. Comput.
, vol.22
, pp. 1444
-
-
Notay, Y.1
-
231
-
-
0001399580
-
An extrapolation process for solving linear systems
-
T. A. Oliphant, An extrapolation process for solving linear systems, Q. Appl. Math. 20, 257 (1962).
-
(1962)
Q. Appl. Math.
, vol.20
, pp. 257
-
-
Oliphant, T.A.1
-
232
-
-
21344440575
-
A new pivoting strategy for Gaussian elimination
-
M. Olschowka and A. Neumaier, A new pivoting strategy for Gaussian elimination, Linear Algebra Its Appl. 240, 131 (1996).
-
(1996)
Linear Algebra Its Appl.
, vol.240
, pp. 131
-
-
Olschowka, M.1
Neumaier, A.2
-
233
-
-
0001644575
-
A block ordering method for sparse matrices
-
J. O'Neil and D. B. SzyId, A block ordering method for sparse matrices, SIAM J. Sci. Stat. Comput. 11, 811 (1990).
-
(1990)
SIAM J. Sci. Stat. Comput.
, vol.11
, pp. 811
-
-
O'Neil, J.1
Szyld, D.B.2
-
234
-
-
0021373623
-
Fast approximate solution of large scale sparse linear systems
-
H. L. Ong, Fast approximate solution of large scale sparse linear systems, J. Comput. Appl. Math. 10, 45 (1984).
-
(1984)
J. Comput. Appl. Math.
, vol.10
, pp. 45
-
-
Ong, H.L.1
-
235
-
-
0035219199
-
Generalized augmented matrix preconditioning approach and its application to iterative solution of ill-conditioned algebraic systems
-
A. Padiy, O. Axelsson, and B. Polman, Generalized augmented matrix preconditioning approach and its application to iterative solution of ill-conditioned algebraic systems, SIAM J. Matrix Anal. Appl. 22, 793 (2001).
-
(2001)
SIAM J. Matrix Anal. Appl.
, vol.22
, pp. 793
-
-
Padiy, A.1
Axelsson, O.2
Polman, B.3
-
236
-
-
0016555955
-
Solution of sparse indefinite systems of linear equations
-
C. C. Paige and M. A. Saunders, Solution of sparse indefinite systems of linear equations, SIAM J. Numer. Anal. 12, 617 (1975).
-
(1975)
SIAM J. Numer. Anal.
, vol.12
, pp. 617
-
-
Paige, C.C.1
Saunders, M.A.2
-
237
-
-
0002058827
-
The numerical solution of parabolic and elliptic differential equations
-
D. W. Peaceman and H. H. Rachford, Jr., The numerical solution of parabolic and elliptic differential equations, J. Soc. Ind. Appl. Math. 3, 28 (1955).
-
(1955)
J. Soc. Ind. Appl. Math.
, vol.3
, pp. 28
-
-
Peaceman, D.W.1
Rachford H.H., Jr.2
-
238
-
-
0023537269
-
Multicolor ICCG methods for vector computers
-
E. L. Poole and J. M. Ortega, Multicolor ICCG methods for vector computers, SIAM J. Numer. Anal. 24, 1394 (1987).
-
(1987)
SIAM J. Numer. Anal.
, vol.24
, pp. 1394
-
-
Poole, E.L.1
Ortega, J.M.2
-
239
-
-
0034734471
-
Global-basis two-level method for indefinite systems. Part 2: Computational issues
-
Y. Qu and J. Fish, Global-basis two-level method for indefinite systems. Part 2: Computational issues, Int. J. Numer. Methods Eng. 49, 461 (2000).
-
(2000)
Int. J. Numer. Methods Eng.
, vol.49
, pp. 461
-
-
Qu, Y.1
Fish, J.2
-
240
-
-
0003715555
-
Domain Decomposition Methods for Partial Differential Equations
-
(Clarendon, Oxford,)
-
A. Quarteroni and A. Valli, Domain Decomposition Methods for Partial Differential Equations (Clarendon, Oxford, 1999).
-
(1999)
-
-
Quarteroni, A.1
Valli, A.2
-
241
-
-
0002655630
-
On the method of conjugate gradients for the solution of large sparse systems of linear equations
-
edited by J. K. Reid (Academic Press, New York,)
-
J. K. Reid, On the method of conjugate gradients for the solution of large sparse systems of linear equations, in Large Sparse Sets of Linear Equations, edited by J. K. Reid, p. 231 (Academic Press, New York, 1971).
-
(1971)
Large Sparse Sets of Linear Equations
, pp. 231
-
-
Reid, J.K.1
-
242
-
-
21444442790
-
A multigrid method based on incomplete Gaussian elimination
-
A. Reusken, A multigrid method based on incomplete Gaussian elimination, Numer. Linear Algebra Appl. 3, 369 (1996).
-
(1996)
Numer. Linear Algebra Appl.
, vol.3
, pp. 369
-
-
Reusken, A.1
-
243
-
-
0012189842
-
Regular incomplete factorizations of real positive definite matrices
-
Y. Robert, Regular incomplete factorizations of real positive definite matrices, Linear Algebra Its Appl. 48, 105 (1982).
-
(1982)
Linear Algebra Its Appl.
, vol.48
, pp. 105
-
-
Robert, Y.1
-
244
-
-
0001885411
-
Algebraic multigrid
-
edited by S. F. McCormick (SIAM, Philadelphia, PA,)
-
J. W. Ruge and K. Stüben, Algebraic multigrid, in Multigrid Methods, edited by S. F. McCormick, p. 73 (SIAM, Philadelphia, PA, 1987).
-
(1987)
Multigrid Methods
, pp. 73
-
-
Ruge, J.W.1
Stüben, K.2
-
245
-
-
0002598644
-
Preconditioning techniques for nonsymmetric and indefinite linear systems
-
Y. Saad, Preconditioning techniques for nonsymmetric and indefinite linear systems, J. Comput. Appl. Math. 24, 89 (1988).
-
(1988)
J. Comput. Appl. Math.
, vol.24
, pp. 89
-
-
Saad, Y.1
-
246
-
-
0001609443
-
Krylov subspace methods on supercomputers
-
Y. Saad, Krylov subspace methods on supercomputers, SIAM J. Sci. Stat. Comput. 10, 1200 (1989).
-
(1989)
SIAM J. Sci. Stat. Comput.
, vol.10
, pp. 1200
-
-
Saad, Y.1
-
247
-
-
0000954680
-
A flexible inner-outer preconditioned GMRES algorithm
-
Y. Saad, A flexible inner-outer preconditioned GMRES algorithm, SIAM J. Sci. Comput. 14, 461 (1993).
-
(1993)
SIAM J. Sci. Comput.
, vol.14
, pp. 461
-
-
Saad, Y.1
-
248
-
-
84985408358
-
ILUT: A dual threshold incomplete LU factorization
-
Y. Saad, ILUT: A dual threshold incomplete LU factorization, Numer. Linear Algebra Appl. 1, 387 (1994).
-
(1994)
Numer. Linear Algebra Appl.
, vol.1
, pp. 387
-
-
Saad, Y.1
-
249
-
-
0001576409
-
Highly parallel preconditioners for general sparse matrices
-
edited by G. H. Golub, R. M. Luskin, and A. Greenbaum IMA Volumes in Mathematics and Its Applications, (Springer-Verlag, New York,)
-
Y. Saad, Highly parallel preconditioners for general sparse matrices, in Recent Advances in Iterative Methods, edited by G. H. Golub, R. M. Luskin, and A. Greenbaum, p. 165, IMA Volumes in Mathematics and Its Applications, Vol. 60 (Springer-Verlag, New York, 1994).
-
(1994)
Recent Advances in Iterative Methods
, vol.60
, pp. 165
-
-
Saad, Y.1
-
250
-
-
0001085784
-
ILUM: A multi-elimination ILU preconditioner for general sparse matrices
-
Y. Saad, ILUM: A multi-elimination ILU preconditioner for general sparse matrices, SIAM J. Sci. Comput. 17, 830 (1996).
-
(1996)
SIAM J. Sci. Comput.
, vol.17
, pp. 830
-
-
Saad, Y.1
-
251
-
-
0003554096
-
Iterative Methods for Sparse Linear Systems
-
(PWS Publishing, Boston,)
-
Y. Saad, Iterative Methods for Sparse Linear Systems (PWS Publishing, Boston, 1996).
-
(1996)
-
-
Saad, Y.1
-
252
-
-
85190756111
-
Finding Exact and Approximate Block Structures for ILU Preconditioning
-
Technical Report UMSI- 2001-93 (Minnesota Supercomputer Institute, Univ. Minnesota, Minneapolis,)
-
Y. Saad, Finding Exact and Approximate Block Structures for ILU Preconditioning, Technical Report UMSI- 2001-93 (Minnesota Supercomputer Institute, Univ. Minnesota, Minneapolis, 2001).
-
(2001)
-
-
Saad, Y.1
-
253
-
-
0000048673
-
GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
-
Y. Saad and M. H. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput. 7, 856 (1986).
-
(1986)
SIAM J. Sci. Stat. Comput.
, vol.7
, pp. 856
-
-
Saad, Y.1
Schultz, M.H.2
-
254
-
-
0012122048
-
ARMS: An algebraic recursive multilevel solver for general sparse linear systems
-
Y. Saad and B. Suchomel, ARMS: An algebraic recursive multilevel solver for general sparse linear systems, Numer. Linear Algebra Appl. 9, 359 (2002).
-
(2002)
Numer. Linear Algebra Appl.
, vol.9
, pp. 359
-
-
Saad, Y.1
Suchomel, B.2
-
255
-
-
0039179703
-
Iterative solution of linear systems in the 20th century
-
Y. Saad and H. A. van der Vorst, Iterative solution of linear systems in the 20th century, J. Comput. Appl. Math. 123, 1 (2000).
-
(2000)
J. Comput. Appl. Math.
, vol.123
, pp. 1
-
-
Saad, Y.1
van der Vorst, H.A.2
-
256
-
-
0033295420
-
BILUM: Block versions of multielimination and multilevel preconditioner for general sparse linear systems
-
Y. Saad and J. Zhang, BILUM: Block versions of multielimination and multilevel preconditioner for general sparse linear systems, SIAM J. Sci. Comput. 20, 2103 (1999).
-
(1999)
SIAM J. Sci. Comput.
, vol.20
, pp. 2103
-
-
Saad, Y.1
Zhang, J.2
-
257
-
-
0033233446
-
BILUTM: A domain-based multilevel block ILUT preconditioner for general sparse matrices
-
Y. Saad and J. Zhang, BILUTM: A domain-based multilevel block ILUT preconditioner for general sparse matrices, SIAM J. Matrix Anal. Appl. 21, 279 (1999).
-
(1999)
SIAM J. Matrix Anal. Appl.
, vol.21
, pp. 279
-
-
Saad, Y.1
Zhang, J.2
-
258
-
-
0030126179
-
High-performance PCG solvers for FEM structural analyses
-
P. Saint-Georges, G. Warzee, Y. Notay, and R. Beauwens, High-performance PCG solvers for FEM structural analyses, Int. J. Numer. Methods Eng. 39, 1133 (1996).
-
(1996)
Int. J. Numer. Methods Eng.
, vol.39
, pp. 1133
-
-
Saint-Georges, P.1
Warzee, G.2
Notay, Y.3
Beauwens, R.4
-
259
-
-
0033207755
-
Problem-dependent preconditioners for iterative solvers in FE elastostatics
-
P. Saint-Georges, G. Warzee, Y. Notay, and R. Beauwens, Problem-dependent preconditioners for iterative solvers in FE elastostatics, Comput. Struct. 73, 33 (1999).
-
(1999)
Comput. Struct.
, vol.73
, pp. 33
-
-
Saint-Georges, P.1
Warzee, G.2
Notay, Y.3
Beauwens, R.4
-
261
-
-
84968487134
-
On the numerical solution of elliptic difference equations
-
J. W. Sheldon, On the numerical solution of elliptic difference equations, Math. Tables Other Aids Comput. 9, 101 (1955).
-
(1955)
Math. Tables Other Aids Comput.
, vol.9
, pp. 101
-
-
Sheldon, J.W.1
-
262
-
-
85190790669
-
Exploiting Multilevel Preconditioning Techniques in Eigenvalue Computations
-
Preprint nr. 1117 (Dep. Mathematics, Univ. Utrecht, Utrecht, The Netherlands, 1999; revised version)
-
G. L. G. Sleijpen and F. W. Wubs, Exploiting Multilevel Preconditioning Techniques in Eigenvalue Computations, Preprint nr. 1117 (Dep. Mathematics, Univ. Utrecht, Utrecht, The Netherlands, 1999; revised version 2001).
-
(2001)
-
-
Sleijpen, G.L.G.1
Wubs, F.W.2
-
263
-
-
0022661211
-
An algorithm for profile and wavefront reduction of sparse matrices
-
S. W. Sloan, An algorithm for profile and wavefront reduction of sparse matrices, Int. J. Numer. Methods Eng. 23, 239 (1986).
-
(1986)
Int. J. Numer. Methods Eng.
, vol.23
, pp. 239
-
-
Sloan, S.W.1
-
264
-
-
0003419897
-
Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations
-
(Cambridge Univ. Press, Cambridge/New York/Melbourne,)
-
B. F. Smith, P. E. Bjørstad, and W. D. Gropp, Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations (Cambridge Univ. Press, Cambridge/New York/Melbourne, 1996).
-
(1996)
-
-
Smith, B.F.1
Bjørstad, P.E.2
Gropp, W.D.3
-
265
-
-
44049110107
-
Parallel ocean general circulation modeling
-
R. D. Smith, J. K. Dukowicz, and R. C. Malone, Parallel ocean general circulation modeling, Phys. D 60, 38 (1992).
-
(1992)
Phys. D
, vol.60
, pp. 38
-
-
Smith, R.D.1
Dukowicz, J.K.2
Malone, R.C.3
-
266
-
-
0002621183
-
Algebraic multigrid (AMG): Experiences and comparisons
-
K. Stüben, Algebraic multigrid (AMG): Experiences and comparisons, Appl. Math. Comput. 13, 419 (1983).
-
(1983)
Appl. Math. Comput.
, vol.13
, pp. 419
-
-
Stüben, K.1
-
267
-
-
0035282142
-
A review of algebraic multigrid
-
K. Stüben, A review of algebraic multigrid, J. Comput. Appl. Math. 128, 281 (2001).
-
(2001)
J. Comput. Appl. Math.
, vol.128
, pp. 281
-
-
Stüben, K.1
-
268
-
-
0000398933
-
A robust incomplete factorization based on value and space constraints
-
M. Suaijana and K. H. Law, A robust incomplete factorization based on value and space constraints, Int. J. Numer. Methods Eng. 38, 1703 (1995).
-
(1995)
Int. J. Numer. Methods Eng.
, vol.38
, pp. 1703
-
-
Suaijana, M.1
Law, K.H.2
-
269
-
-
0036229185
-
FQMR: A flexible quasi-minimal residual method with inexact preconditioning
-
D. B. Szyld and J. Vogel, FQMR: A flexible quasi-minimal residual method with inexact preconditioning, SIAM J. Sci. Comput. 23, 363 (2001).
-
(2001)
SIAM J. Sci. Comput.
, vol.23
, pp. 363
-
-
Szyld, D.B.1
Vogel, J.2
-
270
-
-
0034144756
-
Sparse approximate inverse smoother for multigrid
-
W.-P. Tang and W.-L. Wan, Sparse approximate inverse smoother for multigrid, SIAM J. Matrix Anal. Appl. 21, 1236 (2000).
-
(2000)
SIAM J. Matrix Anal. Appl.
, vol.21
, pp. 1236
-
-
Tang, W.-P.1
Wan, W.-L.2
-
271
-
-
0000425921
-
A new preconditioning technique for solving large sparse linear systems
-
M. Tismenetsky, A new preconditioning technique for solving large sparse linear systems, Linear Algebra Its Appl. 154-156, 331 (1991).
-
(1991)
Linear Algebra Its Appl.
, vol.154-156
, pp. 331
-
-
Tismenetsky, M.1
-
272
-
-
0003424374
-
Numerical Linear Algebra
-
(SIAM, Philadelphia, PA,)
-
L. N. Trefethen and D. Ban, III, Numerical Linear Algebra (SIAM, Philadelphia, PA, 1997).
-
(1997)
-
-
Trefethen, L.N.1
Ban D. III2
-
273
-
-
0004239925
-
Multigrid
-
(Academic Press, London,)
-
U. Trottenberg, C. W. Oosterlee, and A. Schüller, Multigrid (Academic Press, London, 2000).
-
(2000)
-
-
Trottenberg, U.1
Oosterlee, C.W.2
Schüller, A.3
-
274
-
-
0000612851
-
Rounding-off errors in matrix processes
-
A. M. Turing, Rounding-off errors in matrix processes, Q. J. Mech. Appl. Math. 1, 287 (1948).
-
(1948)
Q. J. Mech. Appl. Math.
, vol.1
, pp. 287
-
-
Turing, A.M.1
-
275
-
-
0012163646
-
An Approximate Factorization Procedure Based on the Block Cholesky Decomposition and Its Use with the Conjugate Gradient Method
-
Report NEDO- 11386 (General Electric Co., Nuclear Energy Div., San José, CA,)
-
R. Underwood, An Approximate Factorization Procedure Based on the Block Cholesky Decomposition and Its Use with the Conjugate Gradient Method, Report NEDO- 11386 (General Electric Co., Nuclear Energy Div., San José, CA, 1976).
-
(1976)
-
-
Underwood, R.1
-
276
-
-
0029712143
-
Nested grids ILU-decomposition (NGILU)
-
A. van der Ploeg, E. F. F. Botta, and F. W. Wubs, Nested grids ILU-decomposition (NGILU), J. Comput. Appl. Math. 66, 515 (1996).
-
(1996)
J. Comput. Appl. Math.
, vol.66
, pp. 515
-
-
van der Ploeg, A.1
Botta, E.F.F.2
Wubs, F.W.3
-
277
-
-
0002003127
-
Iterative solution methods for certain sparse linear systems with a nonsymmetric matrix arising from PDE-problems
-
H. A. van der Vorst, Iterative solution methods for certain sparse linear systems with a nonsymmetric matrix arising from PDE-problems, J. Comput. Phys. 44, 1 (1981).
-
(1981)
J. Comput. Phys.
, vol.44
, pp. 1
-
-
van der Vorst, H.A.1
-
278
-
-
0022750329
-
Large tridiagonal and block tridiagonal linear systems on vector and parallel computers
-
H. A. van der Vorst, Large tridiagonal and block tridiagonal linear systems on vector and parallel computers, Parallel Comput. 5, 45 (1987).
-
(1987)
Parallel Comput.
, vol.5
, pp. 45
-
-
van der Vorst, H.A.1
-
279
-
-
0000469387
-
The convergence behaviour of preconditioned CG and CGS in the presence of rounding errors
-
edited by O. Axelsson and L. Yu. Kolotilina Lecture Notes in Mathematics, Vol. 1457 (Springer-Verlag, Berlin,)
-
H. A. van der Vorst, The convergence behaviour of preconditioned CG and CGS in the presence of rounding errors, in Preconditioned Conjugate Gradient Methods, edited by O. Axelsson and L. Yu. Kolotilina, p. 126, Lecture Notes in Mathematics, Vol. 1457 (Springer-Verlag, Berlin, 1990).
-
(1990)
Preconditioned Conjugate Gradient Methods
, pp. 126
-
-
van der Vorst, H.A.1
-
280
-
-
0000005482
-
Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems
-
H. A. van der Vorst, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems, SIAM J. Sci. Star. Comput. 12, 631 (1992).
-
(1992)
SIAM J. Sci. Star. Comput.
, vol.12
, pp. 631
-
-
van der Vorst, H.A.1
-
281
-
-
0002340103
-
Factorizations and normalized iterative methods
-
edited by R. E. Langer, (Univ. Wisconsin Press, Madison,)
-
R. S. Varga, Factorizations and normalized iterative methods, in Boundary Problems in Differential Equations, edited by R. E. Langer, p. 121 (Univ. Wisconsin Press, Madison, 1960).
-
(1960)
Boundary Problems in Differential Equations
, pp. 121
-
-
Varga, R.S.1
-
282
-
-
0003943048
-
Matrix Iterative Analysis
-
(Prentice-Hall, Englewood Cliffs, NJ,)
-
R. S. Varga, Matrix Iterative Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1962).
-
(1962)
-
-
Varga, R.S.1
-
283
-
-
0012126476
-
Incomplete factorizations of matrices and connections with H-matrices
-
R. S. Varga, E. B. Saff, and V. Mehrmann, Incomplete factorizations of matrices and connections with H-matrices, SIAM J. Numer. Anal. 17, 787 (1980).
-
(1980)
SIAM J. Numer. Anal.
, vol.17
, pp. 787
-
-
Varga, R.S.1
Saff, E.B.2
Mehrmann, V.3
-
284
-
-
0031633264
-
A block-factorization (algebraic) formulation of multigrid and Schwarz methods
-
P. S. Vassilevski, A block-factorization (algebraic) formulation of multigrid and Schwarz methods, East-West J. Numer. Math. 6, 65 (1998).
-
(1998)
East-West J. Numer. Math.
, vol.6
, pp. 65
-
-
Vassilevski, P.S.1
-
285
-
-
0032304399
-
Parallelism in ILU-preconditioned GMRES
-
C. Vuik, R. P. van Nooyen, and P. Wesseling, Parallelism in ILU-preconditioned GMRES, Parallel Comput. 24, 1927 (1998).
-
(1998)
Parallel Comput.
, vol.24
, pp. 1927
-
-
Vuik, C.1
van Nooyen, R.P.2
Wesseling, P.3
-
286
-
-
0003735922
-
Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics
-
(Prentice-Hall, Englewood Cliffs, NJ,)
-
E. Wachspress, Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics (Prentice-Hall, Englewood Cliffs, NJ, 1966).
-
(1966)
-
-
Wachspress, E.1
-
288
-
-
0019359208
-
A conjugate gradient truncated direct method for the iterative solution of the reservoir simulation pressure equation
-
J. W. Watts, III, A conjugate gradient truncated direct method for the iterative solution of the reservoir simulation pressure equation, Soc. Petrol. Eng. J. 21, 345 (1981).
-
(1981)
Soc. Petrol. Eng. J.
, vol.21
, pp. 345
-
-
Watts J.W. III1
-
289
-
-
85190761891
-
-
(Akademie, Berlin,)
-
R. Weiss, Parameter-Free Iterative Linear Solvers, Mathematical Research, Vol. 97 (Akademie, Berlin, 1996).
-
(1996)
Parameter-Free Iterative Linear Solvers, Mathematical Research
, vol.97
-
-
Weiss, R.1
-
290
-
-
0000561596
-
On the robustness of ILU-smoothing
-
G. Wittum, On the robustness of ILU-smoothing, SIAM J. Sci. Stat. Comput. 10, 699 (1989).
-
(1989)
SIAM J. Sci. Stat. Comput.
, vol.10
, pp. 699
-
-
Wittum, G.1
-
291
-
-
0012201836
-
Limits on parallelism in the numerical solution of linear PDEs
-
P. H. Worley, Limits on parallelism in the numerical solution of linear PDEs, SIAM J. Sci. Stat. Comput. 12, 1 (1991),
-
(1991)
SIAM J. Sci. Stat. Comput.
, vol.12
, pp. 1
-
-
Worley, P.H.1
-
292
-
-
0001034392
-
Inexact Newton preconditioning techniques for large symmetric eigenvalue problems
-
K. Wu, Y. Saad, and A. Stathopoulos, Inexact Newton preconditioning techniques for large symmetric eigenvalue problems, Electron. Trans. Numer. Anal. 7, 202 (1998).
-
(1998)
Electron. Trans. Numer. Anal.
, vol.7
, pp. 202
-
-
Wu, K.1
Saad, Y.2
Stathopoulos, A.3
-
293
-
-
0003516159
-
Iterative Methods for Solving Partial Difference Equations of Elliptic Type
-
Ph.D. thesis (Harvard University, Cambridge, MA,)
-
D. M. Young, Iterative Methods for Solving Partial Difference Equations of Elliptic Type, Ph.D. thesis (Harvard University, Cambridge, MA, 1950).
-
(1950)
-
-
Young, D.M.1
-
294
-
-
0003677166
-
Iterative Solution of Large Linear systems
-
(Academic Press, New York,)
-
D. M. Young, Iterative Solution of Large Linear systems (Academic Press, New York, 1971).
-
(1971)
-
-
Young, D.M.1
-
295
-
-
0034275112
-
Sparse approximate inverse and multilevel block ILU preconditioning techniques for general sparse matrices
-
J. Zhang, Sparse approximate inverse and multilevel block ILU preconditioning techniques for general sparse matrices, Appl. Numer. Math. 35, 67 (2000).
-
(2000)
Appl. Numer. Math.
, vol.35
, pp. 67
-
-
Zhang, J.1
-
296
-
-
0035219260
-
A multilevel dual reordering strategy for robust incomplete LU factorization of indefinite matrices
-
J. Zhang, A multilevel dual reordering strategy for robust incomplete LU factorization of indefinite matrices, SIAM J. Matrix Anal. Appl. 22, 925 (2001).
-
(2001)
SIAM J. Matrix Anal. Appl.
, vol.22
, pp. 925
-
-
Zhang, J.1
|