-
1
-
-
1842486880
-
A stopping criterion for the conjugate gradient algorithms in a finite element method framework
-
M. Arioli, A stopping criterion for the conjugate gradient algorithms in a finite element method framework, Numer. Math., 97 (2004), pp. 1-24.
-
(2004)
Numer. Math.
, vol.97
, pp. 1-24
-
-
Arioli, M.1
-
3
-
-
0042275964
-
A class of incomplete orthogonal factorization methods. I. Methods and theories
-
Z.-Z. Bai, I. S. Duff, and A. J. Wathen, A class of incomplete orthogonal factorization methods. I. Methods and theories, BIT, 41 (2001), pp. 53-70.
-
(2001)
BIT
, vol.41
, pp. 53-70
-
-
Bai, Z.-Z.1
Duff, I.S.2
Wathen, A.J.3
-
4
-
-
0001644662
-
A bidiagonalization algorithm for solving ill-posed system of linear equations
-
A. Bjorck, A bidiagonalization algorithm for solving ill-posed system of linear equations, BIT, 28 (1988), pp. 659-670.
-
(1988)
BIT
, vol.28
, pp. 659-670
-
-
Bjorck, A.1
-
5
-
-
0003712558
-
Bounds for the error of linear systems of equations using the theory of moments
-
G. Dahlquist, S. C. Eisenstat, and G. H. Golub, Bounds for the error of linear systems of equations using the theory of moments, J. Math. Anal. Appl., 37 (1972), pp. 151-166.
-
(1972)
J. Math. Anal. Appl.
, vol.37
, pp. 151-166
-
-
Dahlquist, G.1
Eisenstat, S.C.2
Golub, G.H.3
-
6
-
-
0003351802
-
Methods of numerical integration
-
Academic Press Inc, Orlando, second ed.
-
P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, Computer Science and Applied Mathematics, Academic Press Inc, Orlando, second ed., 1984.
-
(1984)
Computer Science and Applied Mathematics
-
-
Davis, P.J.1
Rabinowitz, P.2
-
7
-
-
34547488514
-
Algorithm 886: IFISS, aMatlab toolbox for modelling incompressible flow
-
18 pages
-
H. C. Elman, A. Ramage, and D. J. Silvester, Algorithm 886: IFISS, aMatlab toolbox for modelling incompressible flow, ACM Trans. Math. Software, 33 (2007), 14 (18 pages).
-
(2007)
ACM Trans. Math. Software
, vol.33
, pp. 14
-
-
Elman, H.C.1
Ramage, A.2
Silvester, D.J.3
-
8
-
-
33646374284
-
Finite elements and fast iterative solvers: With applications in incompressible fluid dynamics
-
Oxford University Press, New York
-
H. C. Elman, D. J. Silvester, and A. J. Wathen, Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, Numerical Mathematics and Scientific Computation, Oxford University Press, New York, 2005.
-
(2005)
Numerical Mathematics and Scientific Computation
-
-
Elman, H.C.1
Silvester, D.J.2
Wathen, A.J.3
-
9
-
-
0002308279
-
Conjugate gradient methods for indefinite systems
-
Numerical Analysis (Proc 6th Biennial Dundee Conf., Univ. Dundee, Dundee, 1975), G. Watson, ed., Springer, Berlin
-
R. Fletcher, Conjugate gradient methods for indefinite systems, in Numerical Analysis (Proc 6th Biennial Dundee Conf., Univ. Dundee, Dundee, 1975), G. Watson, ed., vol.506 of Lecture Notes in Math., Springer, Berlin, 1976, pp. 73-89.
-
(1976)
Lecture Notes in Math.
, vol.506
, pp. 73-89
-
-
Fletcher, R.1
-
10
-
-
0001378925
-
An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices
-
R. W. Freund, M. H. Gutknecht, and N. M. Nachtigal, An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, SIAM J. Sci. Comput., 14 (1993), pp. 137-158.
-
(1993)
SIAM J. Sci. Comput.
, vol.14
, pp. 137-158
-
-
Freund, R.W.1
Gutknecht, M.H.2
Nachtigal, N.M.3
-
11
-
-
25444452938
-
QMR: A quasi-minimal residual method for non-Hermitian linear systems
-
R. W. Freund and N. M. Nachtigal, QMR: A quasi-minimal residual method for non-Hermitian linear systems, Numer. Math., 60 (1991), pp. 315-339.
-
(1991)
Numer. Math.
, vol.60
, pp. 315-339
-
-
Freund, R.W.1
Nachtigal, N.M.2
-
12
-
-
84968482063
-
Construction of Gauss-Christoffel quadrature formulas
-
W. Gautschi, Construction of Gauss-Christoffel quadrature formulas, Math. Comp., 22 (1968), pp. 251 270.
-
(1968)
Math. Comp.
, vol.22
, pp. 251-270
-
-
Gautschi, W.1
-
13
-
-
0034433978
-
An introduction to the adjoint approach to design
-
M. B. Giles and N. A. P ierce, An introduction to the adjoint approach to design, Flow, Turbulence and Combustion, 65 (2000), pp. 393-415.
-
(2000)
Flow, Turbulence and Combustion
, vol.65
, pp. 393-415
-
-
Giles, M.B.1
Pierce, N.A.2
-
14
-
-
85021895182
-
Adjoint methods for PDEs: A posteriori error analysis and postprocessing by duality
-
M. B. Giles and E. Suli, Adjoint methods for PDEs: A posteriori error analysis and postprocessing by duality, Acta Numer., 11 (2002), pp. 145-236.
-
(2002)
Acta Numer.
, vol.11
, pp. 145-236
-
-
Giles, M.B.1
SUli, E.2
-
15
-
-
0000288016
-
Calculating the singular values and pseudo-inverse ofa matrix
-
B Numer. Anal
-
G. Golub and W. Kahan, Calculating the singular values and pseudo-inverse ofa matrix, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal, 2 (1965), pp. 205-224.
-
(1965)
J. Soc. Indust. Appl. Math. Ser.
, vol.2
, pp. 205-224
-
-
Golub, G.1
Kahan, W.2
-
16
-
-
0001070999
-
Some modified matrix eigenvalue problems
-
G. H. Golub, Some modified matrix eigenvalue problems, SIAM Rev., 15 (1973), pp. 318-334.
-
(1973)
SIAM Rev.
, vol.15
, pp. 318-334
-
-
Golub, G.H.1
-
17
-
-
0041935774
-
Bounds for matrix moments
-
Bounds for matrix moments, Rocky Mountain J. Math., 4 (1974), pp. 207-211.
-
(1974)
Rocky Mountain J. Math.
, vol.4
, pp. 207-211
-
-
-
18
-
-
0003093333
-
Matrices, moments and quadrature
-
(Dundee, 1993), D. Griffiths and G. Watson, eds., vol. 303 of Pitman Res. Notes Math. Ser., Longman Sci. Tech, Harlow
-
G. H. Golub and G. Meurant, Matrices, moments and quadrature, in Numerical Analysis 1993 (Dundee, 1993), D. Griffiths and G. Watson, eds., vol.303 of Pitman Res. Notes Math. Ser., Longman Sci. Tech, Harlow, 1994, pp. 105-156.
-
(1994)
Numerical Analysis 1993
, pp. 105-156
-
-
Golub, G.H.1
Meurant, G.2
-
19
-
-
0000391978
-
Matrices, moments and quadrature. II. How to compute the norm ofthe error in iterative methods
-
G. H. Golub and G. M eurant, Matrices, moments and quadrature. II. How to compute the norm ofthe error in iterative methods, BIT, 37 (1997), pp. 687-705.
-
(1997)
BIT
, vol.37
, pp. 687-705
-
-
Golub, G.H.1
Eurant, G.M.2
-
21
-
-
73349105002
-
Nine ways to compute the scattering cross section (i): Estimating cTx iteratively
-
G. H. Golub, G. N. Minerbo, and P. E. Saylor, Nine ways to compute the scattering cross section (i): Estimating cTx iteratively. Draft, 2007.
-
(2007)
Draft
-
-
Golub, G.H.1
Minerbo, G.N.2
Saylor, P.E.3
-
22
-
-
0001707575
-
The block Lanczos method for computing eigenvalues
-
J. R. Rice, ed., Academic Press, New York
-
G. H. Golub and R. Underwood, The block Lanczos method for computing eigenvalues, in Mathematical software, III (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, 1977), J. R. Rice, ed., Academic Press, New York, 1977, pp. 361-377.
-
(1977)
Mathematical software, III (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, 1977)
, pp. 361-377
-
-
Golub, G.H.1
Underwood, R.2
-
23
-
-
0004168818
-
-
Johns Hopkins University Press, Baltimore, third ed.
-
G. H. Golub and C. F. Van Loan, Matrix Computations, Johns Hopkins Studies in the Mathematical Sciences, Johns Hopkins University Press, Baltimore, third ed., 1996.
-
(1996)
Matrix Computations, Johns Hopkins Studies in the Mathematical Sciences
-
-
Golub, G.H.1
Van Loan, C.F.2
-
24
-
-
0000223746
-
Calculation of Gauss quadrature rules
-
G. H. Golub and J. H. Welsch, Calculation of Gauss quadrature rules, Math. Comp., 23 (1969), pp. 221 230.
-
(1969)
Math. Comp.
, vol.23
, pp. 221-230
-
-
Golub, G.H.1
Welsch, J.H.2
-
26
-
-
0000135303
-
Methods of conjugate gradients for solving linear systems
-
M. R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Stand, 49 (1952), pp. 409-436.
-
(1952)
J. Res. Nat. Bur. Stand
, vol.49
, pp. 409-436
-
-
Hestenes, M.R.1
Stiefel, E.2
-
27
-
-
33846245155
-
Lanczos tridiagonalization and core problems
-
I. Hnetynkova and Z. Strakos, Lanczos tridiagonalization and core problems, Linear Algebra Appl., 421 (2007), pp. 243-251.
-
(2007)
Linear Algebra Appl.
, vol.421
, pp. 243-251
-
-
Hnetynkova, I.1
Strakos, Z.2
-
29
-
-
0141975232
-
A quasi-minimal residual method for simultaneous primal-dual solutions and superconvergent functional estimates
-
J. Lu and D. L. Darmofal, A quasi-minimal residual method for simultaneous primal-dual solutions and superconvergent functional estimates, SIAM J. Sci. Comput., 24 (2003), pp. 1693-1709.
-
(2003)
SIAM J. Sci. Comput.
, vol.24
, pp. 1693-1709
-
-
Lu, J.1
Darmofal, D.L.2
-
31
-
-
0001517599
-
How fast are nonsymmetric matrix iterations
-
N. M. Nachtigal, S. C. Reddy, and L. N. Trefethen, How fast are nonsymmetric matrix iterations?, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 778-795.
-
(1992)
SIAM J. Matrix Anal. Appl.
, vol.13
, pp. 778-795
-
-
Nachtigal, N.M.1
Reddy, S.C.2
Trefethen, L.N.3
-
32
-
-
0016555955
-
Solutions of sparse indefinite systems of linear equations
-
C. C. Paige and M. A. Saunders, Solutions of sparse indefinite systems of linear equations, SIAM J. Numer. Anal, 12 (1975), pp. 617-629.
-
(1975)
SIAM J. Numer. Anal
, vol.12
, pp. 617-629
-
-
Paige, C.C.1
Saunders, M.A.2
-
33
-
-
84976657333
-
Algorithm 583; LSQR: Sparse linear equations and least-squares problems
-
C. C. Paige and M. A. Saunders, Algorithm 583; LSQR: sparse linear equations and least-squares problems, ACM Trans. Math. Software, 8 (1982), pp. 195-209.
-
(1982)
ACM Trans. Math. Software
, vol.8
, pp. 195-209
-
-
Paige, C.C.1
Saunders, M.A.2
-
34
-
-
0039943513
-
LSQR: An algorithm for sparse linear equations and sparse least squares
-
LSQR: an algorithm for sparse linear equations and sparse least squares, ACM Trans. Math. Software, 8 (1982), pp. 43-71.
-
(1982)
ACM Trans. Math. Software
, vol.8
, pp. 43-71
-
-
-
35
-
-
33644601287
-
A class of incomplete orthogonal factorization methods. II. Implementation and results
-
A. T. Papadopoulos, I. S. Duff, and A. J. Wathen, A class ofincomplete orthogonal factorization methods. II. Implementation and results, BIT, 45 (2005), pp. 159-179.
-
(2005)
BIT
, vol.45
, pp. 159-179
-
-
Papadopoulos, A.T.1
Duff, I.S.2
Wathen, A.J.3
-
36
-
-
84966231631
-
A look-ahead Lanczos algorithm for unsymmetric matrices
-
B. N. Parlett, D. R. Taylor, and Z. A. Liu, A look-ahead Lanczos algorithm for unsymmetric matrices, Math. Comp., 44 (1985), pp. 105-124.
-
(1985)
Math. Comp.
, vol.44
, pp. 105-124
-
-
Parlett, B.N.1
Taylor, D.R.2
Liu, Z.A.3
-
38
-
-
21144480809
-
Variational bounds on the entries of the inverse of a matrix
-
P. D. Robinson and A. J. Wathen, Variational bounds on the entries of the inverse of a matrix, IMA J. Numer. Anal., 12 (1992), pp. 463-486.
-
(1992)
IMA J. Numer. Anal.
, vol.12
, pp. 463-486
-
-
Robinson, P.D.1
Wathen, A.J.2
-
39
-
-
1842829625
-
-
Society for Industrial and Applied Mathematics Philadelphia, Second edition
-
Y. Saad, Iterative Methods for Sparse Linear Systems, Society for Industrial and Applied Mathematics, Philadelphia, 2003. Second edition.
-
(2003)
Iterative Methods for Sparse Linear Systems
-
-
Saad, Y.1
-
40
-
-
0010972139
-
Two conjugate-gradient-type methods for unsymmetric linear equations
-
M. A. Saunders, H. D. Simon, and E. L. Yip, Two conjugate-gradient-type methods for unsymmetric linear equations, SIAM J. Numer. Anal, 25 (1988), pp. 927-940.
-
SIAM J. Numer. Anal
, vol.25
, Issue.1988
, pp. 927-940
-
-
Saunders, M.A.1
Simon, H.D.2
Yip, E.L.3
-
41
-
-
0035595411
-
Why Gaussian quadrature in the complex plane? Numer
-
P. E. Saylor and D. C. Smolarski, Why Gaussian quadrature in the complex plane?, Numer. Algorithms, 26 (2001), pp. 251-280.
-
(2001)
Algorithms
, vol.26
, pp. 251-280
-
-
Saylor, P.E.1
Smolarski, D.C.2
-
42
-
-
0035595411
-
Why Gaussian quadrature in the complex plane?
-
Addendum to, Numer. Algorithms 26 (2001), pp. 251-280
-
Addendum to: "Why Gaussian quadrature in the complex plane?" [Numer. Algorithms 26 (2001), pp. 251-280], Numer. Algorithms, 27 (2001), pp. 215-217.
-
(2001)
Numer. Algorithms
, vol.26
, pp. 251-280
-
-
-
43
-
-
0347094766
-
On error estimation in the conjugate gradient method and why it works infinite precision computations
-
Z. StrakoS and P. Tichy, On error estimation in the conjugate gradient method and why it works infinite precision computations, Electron. Trans. Numer. Anal., 13 (2002), pp. 56-80. http://etna.math.kent.edu/vol.13.2 002/pp56-80.dir/.
-
(2002)
Electron. Trans. Numer. Anal.
, vol.13
, pp. 56-80
-
-
StrakoS, Z.1
TichY, P.2
-
44
-
-
29144521333
-
Error estimation in preconditioned conjugate gradients
-
Error estimation in preconditioned conjugate gradients, BIT, 45 (2005), pp. 789-817.
-
(2005)
BIT
, vol.45
, pp. 789-817
-
-
-
46
-
-
0000005482
-
BiCGSTAB: A fast and smoothly converging variant of BiCG for the solution of nonsymmetric linear systems
-
H. A. Van der Vorst, BiCGSTAB: A fast and smoothly converging variant of BiCG for the solution of nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 13 (1992), pp. 631-644.
-
(1992)
SIAM J. Sci. Stat. Comput.
, vol.13
, pp. 631-644
-
-
Van Der Vorst, H.A.1
|