×

zbMATH — the first resource for mathematics

A new look at the Lanczos algorithm for solving symmetric systems of linear equations. (English) Zbl 0431.65016

MSC:
65F10 Iterative numerical methods for linear systems
65-04 Software, source code, etc. for problems pertaining to numerical analysis
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Hestenes, M.R.; Stiefel, E., Methods of conjugate gradients for solving linear systems, J. res. nat. bur. standards, 49, 409-436, (1952) · Zbl 0048.09901
[2] Householder, A.S., The theory of matrices in numerical analysis, (), 139-141 · Zbl 0161.12101
[3] Jennings, A.; Malik, G.A., Partial elimination, J. inst. math. appl., 20, 307-316, (1977) · Zbl 0367.65019
[4] Kahan, W.; Parlett, B.N., How far can you go with the Lanczos algorithm?, () · Zbl 0345.65017
[5] Kaniel, S., Estimates for some computational techniques in linear algebra, Math. comp., 20, 369-378, (1966) · Zbl 0156.16202
[6] Kershaw, D.S., The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations, J. computational phys., 26, 43-65, (1977) · Zbl 0367.65018
[7] Lanczos, C., An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. res. nat. bur. standards, 45, 255-282, (1950)
[8] Lanczos, C., Solution of systems of linear equations by minimized iterations, J. res. nat. bur. standards, 49, 33-53, (1952)
[9] Meijerink, J.A.; van der Vorst, H.A., An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix, Math. comp., 31, 148-162, (1977) · Zbl 0349.65020
[10] Paige, C.C., The computation of eigenvalues and eigenvectors of very large sparse matrices, () · Zbl 0275.65011
[11] Paige, C.C., Computational variants of the Lanczos method for the eigenproblem, J. inst. math. appl., 10, 373-381, (1972) · Zbl 0253.65020
[12] Paige, C.C., Bidiagonalization of matrices and solution of linear equations, (), SIAM J. numer. anal., 11, No. 1, (Mar. 1974)
[13] Paige, C.C.; Saunders, M.A., Solution of sparse indefinite systems of linear equations, SIAM J. numer. anal., 12, 617-629, (1975) · Zbl 0319.65025
[14] Paige, C.C., Error analysis of the Lanczos algorithm for tridiagonalizing a symmetric matrix, J. inst. math. appl., 18, 341-349, (1976) · Zbl 0347.65018
[15] Parlett, B.N.; Scott, D.S., The Lanczos algorithm with selective orthogonalization, Math. comp., 33, 217-238, (1979) · Zbl 0405.65015
[16] Reid, J.K., On the method of conjugate gradients for the solution of large sparse systems of linear equations, () · Zbl 0259.65037
[17] Scott, D.S., Analysis of the symmetric Lanczos process, () · Zbl 0459.65021
[18] Parlett, B.N., ()
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.