-
1
-
-
80052770734
-
Least-squares problems
-
Rutherford Appleton Laboratory, Oxfordshire, UK
-
M. ARIOLI AND S. GRATTON, Least-Squares Problems, Normal Equations, and Stopping Criteria for the Conjugate Gradient Method, Technical Report RAL-TR-2008-008, Rutherford Appleton Laboratory, Oxfordshire, UK, 2008.
-
(2008)
Normal Equations, and Stopping Criteria for the Conjugate Gradient Method, Technical Report RAL-TR-2008-008
-
-
Arioli, M.1
Gratton, S.2
-
2
-
-
0142168839
-
Restrictively preconditioned conjugate gradient methods for systems of linear equations
-
Z.-Z. BAI AND G.-Q. LI, Restrictively preconditioned conjugate gradient methods for systems of linear equations, IMA J. Numer. Anal., 23(2003), pp. 561-580.
-
(2003)
IMA J. Numer. Anal.
, vol.23
, pp. 561-580
-
-
Bai, Z.-Z.1
Li, G.-Q.2
-
3
-
-
0036867930
-
Preconditioning techniques for large linear systems: A survey
-
DOI 10.1006/jcph.2002.7176
-
M. BENZI, Preconditioning techniques for large linear systems: A survey, J. Comput. Phys., 182(2002), pp. 418-477. (Pubitemid 36010064)
-
(2002)
Journal of Computational Physics
, vol.182
, Issue.2
, pp. 418-477
-
-
Benzi, M.1
-
4
-
-
84924279160
-
-
2nd ed., Princeton University Press, Princeton, NJ
-
D. S. BERNSTEIN, Matrix Mathematics: Theory, Facts, and Formulas, 2nd ed., Princeton University Press, Princeton, NJ, 2009.
-
(2009)
Matrix Mathematics: Theory, Facts, and Formulas
-
-
Bernstein, D.S.1
-
5
-
-
0035537405
-
Accurate solution of weighted least squares by iterative methods
-
E. Y. BOBROVNIKOVA AND S. A. VAVASIS, Accurate solution of weighted least squares by iterative methods, SIAM J. Matrix Anal. Appl., 22(2001), pp. 1153-1174.
-
(2001)
SIAM J. Matrix Anal. Appl.
, vol.22
, pp. 1153-1174
-
-
Bobrovnikova, E.Y.1
Vavasis, S.A.2
-
7
-
-
72449121807
-
Stopping criteria for the iterative solution of linear least squares problems
-
X.-W. CHANG, C. C. PAIGE, AND D. TITLEY-PELOQUIN, Stopping criteria for the iterative solution of linear least squares problems, SIAM J. Matrix Anal. Appl., 31(2009), pp. 831-852.
-
(2009)
SIAM J. Matrix Anal. Appl.
, vol.31
, pp. 831-852
-
-
Chang, X.-W.1
Paige, C.C.2
Titley-Peloquin, D.3
-
8
-
-
0034385282
-
Balancing sparse matrices for computing eigenvalues
-
T.-Y. CHEN AND J. W. DEMMEL, Balancing sparse matrices for computing eigenvalues, Linear Algebra Appl., 309(2000), pp. 261-287.
-
(2000)
Linear Algebra Appl.
, vol.309
, pp. 261-287
-
-
Chen, T.-Y.1
Demmel, J.W.2
-
10
-
-
33748139100
-
-
S.-C. CHOI, D. L. DONOHO, A. G. FLESIA, X. HUO, O. LEVI, AND D. SHI, About Beamlab-A Toolbox for New Multiscale Methodologies, http://www-stat. stanford.edu/~beamlab/, 2002.
-
(2002)
About Beamlab - A Toolbox for New Multiscale Methodologies
-
-
Choi, S.-C.1
Donoho, D.L.2
Flesia, A.G.3
Huo, X.4
Levi, O.5
Shi, D.6
-
12
-
-
0032203627
-
Minres and minerr are better than SYMMLQ in eigenpair computations
-
PII S106482759528226X
-
F. A. DUL, MINRES and MINERR are better than SYMMLQ in eigenpair computations, SIAM J. Sci. Comput., 19(1998), pp. 1767-1782. (Pubitemid 128614418)
-
(1998)
SIAM Journal of Scientific Computing
, vol.19
, Issue.6
, pp. 1767-1782
-
-
Dul, F.A.1
-
13
-
-
0000565315
-
Algorithms for the regularization of ill-conditioned least squares problems
-
L. ELDÉN, Algorithms for the regularization of ill-conditioned least squares problems, Nordisk Tidskr. Informationsbehandling (BIT), 17(1977), pp. 134-145.
-
(1977)
Nordisk Tidskr. Informationsbehandling (BIT)
, vol.17
, pp. 134-145
-
-
Eldén, L.1
-
14
-
-
0000382130
-
Minimum residual methods for augmented systems
-
B. FISCHER, A. RAMAGE, D. J. SILVESTER, AND A. J. WATHEN, Minimum residual methods for augmented systems, BIT, 38(1998), pp. 527-543. (Pubitemid 128437154)
-
(1998)
BIT Numerical Mathematics
, vol.38
, Issue.3
, pp. 527-543
-
-
Fischer, B.1
Ramage, A.2
Silvester, D.J.3
Wathen, A.J.4
-
15
-
-
0002971057
-
A new Krylov-subspace method for symmetric indefinite linear systems
-
W. F. Ames, ed., IMACS
-
R. W. FREUND AND N. M. NACHTIGAL, A new Krylov-subspace method for symmetric indefinite linear systems, in Proceedings of the 14th IMACS World Congress on Computational and Applied Mathematics, W. F. Ames, ed., IMACS, 1994, pp. 1253-1256.
-
(1994)
Proceedings of the 14th IMACS World Congress on Computational and Applied Mathematics
, pp. 1253-1256
-
-
Freund, R.W.1
Nachtigal, N.M.2
-
16
-
-
4243859385
-
High performance algorithms for Toeplitz and block Toeplitz matrices
-
K. A. GALLIVAN, S. THIRUMALAI, P. VAN DOOREN, AND V. VERMAUT, High performance algorithms for Toeplitz and block Toeplitz matrices, Linear Algebra Appl., 241/243(1996), pp. 343-388.
-
(1996)
Linear Algebra Appl.
, vol.241-243
, pp. 343-388
-
-
Gallivan, K.A.1
Thirumalai, S.2
Van Dooren, P.3
Vermaut, V.4
-
17
-
-
0000620128
-
Preconditioners for indefinite systems arising in optimization
-
P. E. GILL, W. MURRAY, D. B. PONCELEÓN, AND M. A. SAUNDERS, Preconditioners for indefinite systems arising in optimization, SIAM J. Matrix Anal. Appl., 13(1992), pp. 292-311.
-
(1992)
SIAM J. Matrix Anal. Appl.
, vol.13
, pp. 292-311
-
-
Gill, P.E.1
Murray, W.2
Ponceleón, D.B.3
Saunders, M.A.4
-
18
-
-
0004236492
-
-
3rd ed., Johns Hopkins University Press, Baltimore, MD
-
G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 3rd ed., Johns Hopkins University Press, Baltimore, MD, 1996.
-
(1996)
Matrix Computations
-
-
Golub, G.H.1
Van Loan, C.F.2
-
19
-
-
0002500486
-
Sur les problèmes aux dérivées partielles et leur signification physique
-
J. HADAMARD, Sur les problèmes aux dérivées partielles et leur signification physique, Princeton Univ. Bull., 13(1902), pp. 49-52.
-
(1902)
Princeton Univ. Bull.
, vol.13
, pp. 49-52
-
-
Hadamard, J.1
-
20
-
-
0035074968
-
Iterative methods for nearly singular linear systems
-
W. W. HAGER, Iterative methods for nearly singular linear systems, SIAM J. Sci. Comput., 22(2000), pp. 747-766.
-
(2000)
SIAM J. Sci. Comput.
, vol.22
, pp. 747-766
-
-
Hager, W.W.1
-
21
-
-
0000137080
-
Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques
-
M. HANKE AND J. G. NAGY, Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques, Inverse Problems, 12(1996), pp. 157-173. (Pubitemid 126636637)
-
(1996)
Inverse Problems
, vol.12
, Issue.2
, pp. 157-173
-
-
Hanke, M.1
Nagy, J.G.2
-
22
-
-
0000374864
-
Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank
-
P. C. HANSEN, Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank, SIAM J. Sci. Statist. Comput., 11(1990), pp. 503-518.
-
(1990)
SIAM J. Sci. Statist. Comput.
, vol.11
, pp. 503-518
-
-
Hansen, P.C.1
-
23
-
-
0001632418
-
The use of the L-curve in the regularization of discrete ill-posed problems
-
P. C. HANSEN AND D. P. O'LEARY, The use of the L-curve in the regularization of discrete ill-posed problems, SIAM J. Sci. Comput., 14(1993), pp. 1487-1503.
-
(1993)
SIAM J. Sci. Comput.
, vol.14
, pp. 1487-1503
-
-
Hansen, P.C.1
O'Leary, D.P.2
-
24
-
-
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. Standards, 49(1952), pp. 409-436.
-
(1952)
J. Res. Nat. Bur. Standards
, vol.49
, pp. 409-436
-
-
Hestenes, M.R.1
Stiefel, E.2
-
25
-
-
0036457301
-
-
2nd ed., SIAM, Philadelphia, PA
-
N. J. HIGHAM, Accuracy and Stability of Numerical Algorithms, 2nd ed., SIAM, Philadelphia, PA, 2002.
-
(2002)
Accuracy and Stability of Numerical Algorithms
-
-
Higham, N.J.1
-
27
-
-
0001595571
-
Preconditioned conjugate gradients for solving singular systems
-
E. F. KAASSCHIETER, Preconditioned conjugate gradients for solving singular systems, J. Comput. Appl. Math., 24(1988), pp. 265-275.
-
(1988)
J. Comput. Appl. Math.
, vol.24
, pp. 265-275
-
-
Kaasschieter, E.F.1
-
28
-
-
80052768181
-
-
Ph. D. thesis, SCCM Program, Stanford University, Stanford, CA
-
KAUSTUV, IPSOL: An Interior Point Solver for Nonconvex Optimization Problems, Ph. D. thesis, SCCM Program, Stanford University, Stanford, CA, 2008.
-
(2008)
An Interior Point Solver for Nonconvex Optimization Problems
-
-
Kaustuv, I.1
-
30
-
-
0000094594
-
An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
-
C. LANCZOS, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Res. Nat. Bur. Standards, 45(1950), pp. 255-282.
-
(1950)
J. Res. Nat. Bur. Standards
, vol.45
, pp. 255-282
-
-
Lanczos, C.1
-
33
-
-
4043094131
-
Scaling by binormalization
-
DOI 10.1023/B:NUMA.0000016606.32820.69
-
O. E. LIVNE AND G. H. GOLUB, Scaling by binormalization, Numer. Algorithms, 35(2004), pp. 97-120. (Pubitemid 39072772)
-
(2004)
Numerical Algorithms
, vol.35
, Issue.1
, pp. 97-120
-
-
Livne, O.E.1
Golub, G.H.2
-
34
-
-
0034497397
-
Note on preconditioning for indefinite linear systems
-
DOI 10.1137/S1064827599355153
-
M. F. MURPHY, G. H. GOLUB, AND A. J. WATHEN, A note on preconditioning for indefinite linear systems, SIAM J. Sci. Comput., 21(2000), pp. 1969-1972. (Pubitemid 32076050)
-
(2000)
SIAM Journal of Scientific Computing
, vol.21
, Issue.6
, pp. 1969-1972
-
-
Murphy, M.F.1
Golub, G.H.2
Wathen, A.J.3
-
35
-
-
0012873412
-
Preconditioning of indefinite and almost singular finite element elliptic equations
-
PII S1064827595291480
-
M. G. NEYTCHEVA AND P. S. VASSILEVSKI, Preconditioning of indefinite and almost singular finite element elliptic equations, SIAM J. Sci. Comput., 19(1998), pp. 1471-1485. (Pubitemid 128623558)
-
(1998)
SIAM Journal of Scientific Computing
, vol.19
, Issue.5
, pp. 1471-1485
-
-
Neytcheva, M.G.1
Vassilevski, P.S.2
-
37
-
-
0000293926
-
Solving positive (semi) definite linear systems by preconditioned iterative methods
-
Lecture Notes in Math, Springer, Berlin
-
Y. NOTAY, Solving positive (semi) definite linear systems by preconditioned iterative methods, in Preconditioned Conjugate Gradient Methods (Nijmegen, 1989), Lecture Notes in Math. 1457, Springer, Berlin, 1990, pp. 105-125.
-
(1990)
Preconditioned Conjugate Gradient Methods (Nijmegen, 1989)
, vol.1457
, pp. 105-125
-
-
Notay, Y.1
-
38
-
-
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
-
39
-
-
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(1975), pp. 617-629.
-
(1975)
SIAM J. Numer. Anal.
, vol.12
, pp. 617-629
-
-
Paige, C.C.1
Saunders, M.A.2
-
40
-
-
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. Software, 8(1982), pp. 43-71.
-
(1982)
ACM Trans. Math. Software
, vol.8
, pp. 43-71
-
-
Paige, C.C.1
Saunders, M.A.2
-
41
-
-
84976657333
-
Algorithm 583; LSQR: Sparse linear equations and leastsquares prob lems
-
C. C. PAIGE AND M. A. SAUNDERS, Algorithm 583; LSQR: Sparse linear equations and leastsquares prob lems, 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
-
42
-
-
14544272196
-
Iterative methods with preconditioners for indefinite systems
-
W.-Q. REN AND J.-X. ZHAO, Iterative methods with preconditioners for indefinite systems, J. Comput. Math., 17(1999), pp. 89-96.
-
(1999)
J. Comput. Math.
, vol.17
, pp. 89-96
-
-
Ren, W.-Q.1
Zhao, J.-X.2
-
43
-
-
0344950439
-
Krylov subspace methods for saddle point problems with indefinite preconditioning
-
DOI 10.1137/S0895479800375540, PII S0895479800375540
-
M. ROZLOŽNÍK AND V. SIMONCINI, Krylov subspace methods for saddle point problems with indefinite preconditioning, SIAM J. Matrix Anal. Appl., 24(2002), pp. 368-391. (Pubitemid 36446414)
-
(2003)
SIAM Journal on Matrix Analysis and Applications
, vol.24
, Issue.2
, pp. 368-391
-
-
Rozloznik, M.1
Simoncini, V.2
-
44
-
-
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. Statist. Comput., 7(1986), pp. 856-869.
-
(1986)
SIAM J. Sci. Statist. Comput.
, vol.7
, pp. 856-869
-
-
Saad, Y.1
Schultz, M.H.2
-
45
-
-
0000307001
-
Solution of sparse rectangular systems using LSQR and Craig
-
M. A. SAUNDERS, Solution of sparse rectangular systems using LSQR and Craig, BIT, 35(1995), pp. 588-604.
-
(1995)
BIT
, vol.35
, pp. 588-604
-
-
Saunders, M.A.1
-
46
-
-
0005462653
-
Computing projections with LSQR
-
M. A. SAUNDERS, Computing projections with LSQR, BIT, 37(1997), pp. 96-104. (Pubitemid 127485204)
-
(1997)
BIT Numerical Mathematics
, vol.37
, Issue.1
, pp. 96-104
-
-
Saunders, M.A.1
-
47
-
-
0035219272
-
Differences in the effects of rounding errors in Krylov solvers for symmetric indefinite linear systems
-
G. L. G. SLEIJPEN, H. A. VAN der VORST, AND J. MODERSITZKI, Differences in the effects of rounding errors in Krylov solvers for symmetric indefinite linear systems, SIAM J. Matrix Anal. Appl., 22(2000), pp. 726-751.
-
(2000)
SIAM J. Matrix Anal. Appl.
, vol.22
, pp. 726-751
-
-
Sleijpen, G.L.G.1
Van Der Vorst, H.A.2
Modersitzki, J.3
-
48
-
-
0013440801
-
On the continuity of the generalized inverse
-
G. W. STEWART, On the continuity of the generalized inverse, SIAM J. Appl. Math., 17(1969), pp. 33-45.
-
(1969)
SIAM J. Appl. Math.
, vol.17
, pp. 33-45
-
-
Stewart, G.W.1
-
49
-
-
0012096219
-
Research, development and LINPACK
-
J. R. Rice, ed., Academic Press, New York
-
G. W. STEWART, Research, development and LINPACK, in Mathematical Software III, J. R. Rice, ed., Academic Press, New York, 1977, pp. 1-14.
-
(1977)
Mathematical Software III
, pp. 1-14
-
-
Stewart, G.W.1
-
50
-
-
0033279732
-
QLP approximation to the singular value decomposition
-
DOI 10.1137/S1064827597319519
-
G. W. STEWART, The QLP approximation to the singular value decomposition, SIAM J. Sci. Comput., 20(1999), pp. 1336-1348. (Pubitemid 32251220)
-
(1999)
SIAM Journal of Scientific Computing
, vol.20
, Issue.4
, pp. 1336-1348
-
-
Stewart, G.W.1
-
51
-
-
80052695145
-
-
Stanford University, downloadable software
-
Systems Optimization Laboratory (SOL), Stanford University, downloadable software, http://www.stanford.edu/group/SOL/software.html.
-
Systems Optimization Laboratory (SOL)
-
-
-
52
-
-
3142570751
-
Block preconditioners for symmetric indefinite linear systems
-
DOI 10.1002/nme.982
-
K.-C. TOH, K.-K. PHOON, AND S.-H. CHAN, Block preconditioners for symmetric indefinite linear systems, Internat. J. Numer. Methods Engrg., 60(2004), pp. 1361-1381. (Pubitemid 38904857)
-
(2004)
International Journal for Numerical Methods in Engineering
, vol.60
, Issue.8
, pp. 1361-1381
-
-
Toh, K.-C.1
Phoon, K.-K.2
Chan, S.-H.3
-
53
-
-
0003424374
-
-
SIAM, Philadelphia, PA
-
L. N. TREFETHEN AND D. BAU, III, Numerical Linear Algebra, SIAM, Philadelphia, PA, 1997.
-
(1997)
Numerical Linear Algebra
-
-
Trefethen, L.N.1
Bau III, D.2
-
55
-
-
0032303559
-
Solving large-scale linear programs by interior-point methods under the MATLAB environment
-
Y. ZHANG, Solving large-scale linear programs by interior-point methods under the MATLAB environment, Optim. Methods Softw., 10(1998), pp. 1-31.
-
(1998)
Optim. Methods Softw.
, vol.10
, pp. 1-31
-
-
Zhang, Y.1
|