-
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
-
2
-
-
0000015959
-
Solving sparse, linear systems with sparse backward error
-
M. Arioli, J. W. Demmel and I. S. Duff, Solving sparse, linear systems with sparse backward error, SIAM J. Matrix Anal. Appl., 10 (1989), pp. 165-190.
-
(1989)
SIAM J. Matrix Anal. Appl.
, vol.10
, pp. 165-190
-
-
Arioli, M.1
Demmel, J.W.2
Duff, I.S.3
-
3
-
-
0002918288
-
Stopping criteria for iterative solvers
-
M. Arioli, I. Duff and D. Ruiz, Stopping criteria for iterative solvers, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 138-144.
-
(1992)
SIAM J. Matrix Anal. Appl.
, vol.13
, pp. 138-144
-
-
Arioli, M.1
Duff, I.2
Ruiz, D.3
-
4
-
-
0005582193
-
Stopping criteria for iterative methods: Applications to PDE's
-
M. Arioli, E. Noulard and A. Russo, Stopping criteria for iterative methods: applications to PDE's, Calcolo, 38 (2001), pp. 97-112.
-
(2001)
Calcolo
, vol.38
, pp. 97-112
-
-
Arioli, M.1
Noulard, E.2
Russo, A.3
-
6
-
-
0035625586
-
Error norm estimation and stopping criteria in preconditioned conjugate gradient iterations
-
O. Axelsson and I. Kaporin, Error norm estimation and stopping criteria in preconditioned conjugate gradient iterations, Numer. Linear Algebra Appl., 8 (2001), pp. 265-286.
-
(2001)
Numer. Linear Algebra Appl.
, vol.8
, pp. 265-286
-
-
Axelsson, O.1
Kaporin, I.2
-
7
-
-
18744383413
-
Mathematics of the verification and validation in computational engineering
-
M. Kočandrlová and V. Kelar, eds., Union of Czech Mathematicians and Physicists, Prague
-
I. Babuška, Mathematics of the verification and validation in computational engineering, in Mathematical and Computer Modelling in Science and Engineering, M. Kočandrlová and V. Kelar, eds., pp. 5-12, Union of Czech Mathematicians and Physicists, Prague, 2003.
-
(2003)
Mathematical and Computer Modelling in Science and Engineering
, pp. 5-12
-
-
Babuška, I.1
-
8
-
-
0003473816
-
-
SIAM, Philadelphia, PA
-
R. Barrett, M. Berry, T. F. Chan et al., Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia, PA, 1994.
-
(1994)
Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods
-
-
Barrett, R.1
Berry, M.2
Chan, T.F.3
-
9
-
-
1842535089
-
Solving large-scale control problems
-
to appear in
-
P. Benner, Solving large-scale control problems, to appear in IEEE Control Syst. Magazine, 24 (2004), pp. 44-59.
-
(2004)
IEEE Control Syst. Magazine
, vol.24
, pp. 44-59
-
-
Benner, P.1
-
10
-
-
0003712558
-
Bounds for the error of linear systems of equations using the theory of moments
-
G. Dahlquist, S. 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.2
Golub, G.H.3
-
11
-
-
0041590254
-
Bounds for the error in linear systems
-
R. Hettich, ed., Springer, Berlin
-
G. Dahlquist, G. H. Golub and S. G. Nash, Bounds for the error in linear systems, in Proc. Workshop on Semi-Infinite Programming, R. Hettich, ed., pp. 154-172, Springer, Berlin, 1978.
-
(1978)
Proc. Workshop on Semi-infinite Programming
, pp. 154-172
-
-
Dahlquist, G.1
Golub, G.H.2
Nash, S.G.3
-
12
-
-
0003043091
-
Cascadic conjugate, gradient methods for elliptic partial differential equations: Algorithm and numerical results
-
Domain decomposition methods in scientific and engineering computing (University Park, PA, 1993), Am. Math. Soc., Providence, RI
-
P. Deuflhard, Cascadic conjugate, gradient methods for elliptic partial differential equations: algorithm and numerical results, in Domain decomposition methods in scientific and engineering computing (University Park, PA, 1993), Contemp. Math., vol. 180, pp. 29-42, Am. Math. Soc., Providence, RI, 1994.
-
(1994)
Contemp. Math.
, vol.180
, pp. 29-42
-
-
Deuflhard, P.1
-
13
-
-
2942715626
-
-
TR/PA/03/3, CERFACS, Toulouse Cedex, France
-
V. Frayssé, L. Giraud, S. Gratton and J. Langou, A set of GMRES routines for real and complex arithmetics on on high performance computers, TR/PA/03/3, CERFACS, Toulouse Cedex, France, 2003.
-
(2003)
A Set of GMRES Routines for Real and Complex Arithmetics on on High Performance Computers
-
-
Frayssé, V.1
Giraud, L.2
Gratton, S.3
Langou, J.4
-
14
-
-
0003093333
-
Matrices, moments and quadrature
-
June 1993, D. Sciffeths and G. Watson, eds., Longman Sci. Tech. Publ.
-
G. H. Golub and G. Meurant, Matrices, moments and quadrature, in Proc. 15-th Dundee Conf., June 1993, D. Sciffeths and G. Watson, eds., pp. 106-166, Longman Sci. Tech. Publ., 1994.
-
(1994)
Proc. 15-th Dundee Conf.
, pp. 106-166
-
-
Golub, G.H.1
Meurant, G.2
-
15
-
-
0000391978
-
Matrices, moments and quadrature. II. How to compute the norm of the error in iterative methods
-
G. H. Golub and G. Meurant, Matrices, moments and quadrature. II. How to compute the norm of the error in iterative methods, BIT, 37 (1997), pp. 687-706.
-
(1997)
BIT
, vol.37
, pp. 687-706
-
-
Golub, G.H.1
Meurant, G.2
-
16
-
-
0000918880
-
Estimates in quadratic formulas
-
G. H. Golub and Z. Strakoš, Estimates in quadratic formulas, Numer. Algorithms, 8 (1994), pp. 241-268.
-
(1994)
Numer. Algorithms
, vol.8
, pp. 241-268
-
-
Golub, G.H.1
Strakoš, Z.2
-
17
-
-
0004236492
-
-
The Johns Hopkins University Press, Baltimore MD, third edn.
-
G. H. Golub and C. van Loan, Matrix Computation, The Johns Hopkins University Press, Baltimore MD, third edn., 1996.
-
(1996)
Matrix Computation
-
-
Golub, G.H.1
Van Loan, C.2
-
18
-
-
0002362050
-
Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences
-
A. Greenbaum, Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences, Linear Algebra Appl., 113 (1989), pp. 7-63.
-
(1989)
Linear Algebra Appl.
, vol.113
, pp. 7-63
-
-
Greenbaum, A.1
-
19
-
-
0031495031
-
Estimating the attainable accuracy of recursively computed residual methods
-
A. Greenbaum, Estimating the attainable accuracy of recursively computed residual methods, SIAM J. Matrix Anal. Appl., 18 (1997), pp. 535-551.
-
(1997)
SIAM J. Matrix Anal. Appl.
, vol.18
, pp. 535-551
-
-
Greenbaum, A.1
-
20
-
-
0003241196
-
Iterative methods for solving linear systems
-
SIAM, Philadelphia, PA.
-
A. Greenbaum, Iterative methods for solving linear systems, Frontiers in Applied Mathematics, vol. 17, SIAM, Philadelphia, PA., 1997.
-
(1997)
Frontiers in Applied Mathematics
, vol.17
-
-
Greenbaum, A.1
-
21
-
-
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 (1992), pp. 121-137.
-
(1992)
SIAM J. Matrix Anal. Appl.
, vol.13
, pp. 121-137
-
-
Greenbaum, A.1
Strakoš, Z.2
-
22
-
-
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. Bureau Stand., 49 (1952), pp. 409-435.
-
(1952)
J. Res. Nat. Bureau Stand.
, vol.49
, pp. 409-435
-
-
Hestenes, M.R.1
Stiefel, E.2
-
24
-
-
29144525889
-
-
Laboratory of Structural Mechanics, Finland, May. Matrix Market
-
R. Kouhia, Description of the CYLSHELL set, Laboratory of Structural Mechanics, Finland, May 1998. Matrix Market.
-
(1998)
Description of the CYLSHELL Set
-
-
Kouhia, R.1
-
25
-
-
29144467549
-
-
Matrix Market, http://math.nist.gov/MatrixMarket/. The Matrix Market is a service of the Mathematical and Computational Sciences Division of the Information Technology Laboratory of the National Institute of Standards and Technology.
-
-
-
-
26
-
-
0003324046
-
Computer solution of large linear systems
-
North-Holland Publishing Co., Amsterdam
-
G. Meurant, Computer solution of large linear systems, Studies in Mathematics and its Applications, vol. 28, North-Holland Publishing Co., Amsterdam, 1999.
-
(1999)
Studies in Mathematics and Its Applications
, vol.28
-
-
Meurant, G.1
-
27
-
-
0043138868
-
Numerical experiments in computing bounds for the norm of the error in the preconditioned conjugate gradient algorithm
-
G. Meurant, Numerical experiments in computing bounds for the norm of the error in the preconditioned conjugate gradient algorithm, Numer. Algorithms 22, 3-4 (1999), pp. 353-365.
-
(1999)
Numer. Algorithms
, vol.22
, Issue.3-4
, pp. 353-365
-
-
Meurant, G.1
-
28
-
-
29144502943
-
Towards a reliable implementation of the conjugate gradient method
-
Invited plenary lecture, Zurich, February
-
G. Meurant, Towards a reliable implementation of the conjugate gradient method, Invited plenary lecture at the Latsis Symposium: Iterative Solvers for Large Linear Systems, Zurich, February 2002.
-
(2002)
Latsis Symposium: Iterative Solvers for Large Linear Systems
-
-
Meurant, G.1
-
29
-
-
24944444341
-
-
pubblicazioni n. 956, Instituto di Analisi Numerica, Pavia, Italy
-
E. Noulard and M. Arioli, Vector stopping criteria for iterative methods: Theoretical tools, pubblicazioni n. 956, Instituto di Analisi Numerica, Pavia, Italy, 1995.
-
(1995)
Vector Stopping Criteria for Iterative Methods: Theoretical Tools
-
-
Noulard, E.1
Arioli, M.2
-
30
-
-
33845220799
-
Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides
-
W. Oettli and W. Prager, Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides, Numer. Math., 6 (1964), pp. 405-409.
-
(1964)
Numer. Math.
, vol.6
, pp. 405-409
-
-
Oettli, W.1
Prager, W.2
-
31
-
-
53849148874
-
Error analysis of the lanczos algorithm for tridiagonalizing a symmetric matrix
-
C. C. Paige, Error analysis of the lanczos algorithm for tridiagonalizing a symmetric matrix, J. Inst. Math. Appl, 18 (1976), pp. 341-349.
-
(1976)
J. Inst. Math. Appl
, vol.18
, pp. 341-349
-
-
Paige, C.C.1
-
32
-
-
0039943513
-
LSQR: An algorithm for sparse linear equations and sparse least squares
-
C. C. Paige and M. A. Saunders, LSQR: an algorithm for sparse linear equations and sparse least squares, ACM Trans. Math. Softw., 8 (1982), pp. 43-71.
-
(1982)
ACM Trans. Math. Softw.
, vol.8
, pp. 43-71
-
-
Paige, C.C.1
Saunders, M.A.2
-
33
-
-
0036447618
-
Residual and backward error bounds in minimum residual Krylov subspace methods
-
electronic
-
C. C. Paige and Z. Strakoš, Residual and backward error bounds in minimum residual Krylov subspace methods, SIAM J. Sci. Comput., 23 (2002), pp. 1898-1923 (electronic).
-
(2002)
SIAM J. Sci. Comput.
, vol.23
, pp. 1898-1923
-
-
Paige, C.C.1
Strakoš, Z.2
-
34
-
-
1842829625
-
-
SIAM, Philadelphia, PA, second edn.
-
Y. Saad, Iterative Methods for Sparse Linear Systems, SIAM, Philadelphia, PA, second edn., 2003.
-
(2003)
Iterative Methods for Sparse Linear Systems
-
-
Saad, Y.1
-
35
-
-
84966248432
-
Iterative refinement implies numerical stability for Gaussian elimination
-
R. D. Skeel, Iterative refinement implies numerical stability for Gaussian elimination, Math. Comp., 35 (1980), pp. 817-832.
-
(1980)
Math. Comp.
, vol.35
, pp. 817-832
-
-
Skeel, R.D.1
-
36
-
-
0002777912
-
BiCGstab(l) and other hybrid Bi-CG methods
-
G. L. G. Sleijpen, H. A. van der Vorst and D. R. Fokkema, BiCGstab(l) and other hybrid Bi-CG methods, Numer. Algorithms, 7 (1994), pp. 75-109.
-
(1994)
Numer. Algorithms
, vol.7
, pp. 75-109
-
-
Sleijpen, G.L.G.1
Van Der Vorst, H.A.2
Fokkema, D.R.3
-
37
-
-
0011980184
-
-
thesis for the degree doctor of science, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, February
-
Z. Strakoš, Theory of Convergence and Effects of Finite Precision Arithmetic in Krylov Subspace Methods, thesis for the degree doctor of science, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, February 2001.
-
(2001)
Theory of Convergence and Effects of Finite Precision Arithmetic in Krylov Subspace Methods
-
-
Strakoš, Z.1
-
38
-
-
0347094766
-
On error estimation in the conjugate gradient method and why it works in finite precision computations
-
electronic
-
Z. Strakoš and P. Tichý On error estimation in the conjugate gradient method and why it works in finite precision computations, Electron. Trans. Numer. Anal., 13 (2002), pp. 66-80 (electronic).
-
(2002)
Electron. Trans. Numer. Anal.
, vol.13
, pp. 66-80
-
-
Strakoš, Z.1
Tichý, P.2
-
39
-
-
18744404874
-
On estimation of the A-norm of the error in CG and PCG
-
published online
-
Z. Strakoš and P. Tichý, On estimation of the A-norm of the error in CG and PCG, PAMM, 3 (2003), pp. 553-554 (published online).
-
(2003)
PAMM
, vol.3
, pp. 553-554
-
-
Strakoš, Z.1
Tichý, P.2
|