Document Zbl 0515.65036

Numerical aspects of Gram-Schmidt orthogonalization of vectors. (English) Zbl 0515.65036

Linear Algebra Appl. 52-53, 591-601 (1983).

Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0515.65036

MSC:

65F25	Orthogonalization in numerical linear algebra
65F15	Numerical computation of eigenvalues and eigenvectors of matrices

Keywords:

Gram-Schmidt orthogonalization; Gauss-Jacobi and Gauss-Seidel iterations; biorthogonalization; oblique projections; Krylov subspace; eigenvalues

Software:

LINPACK

Cite Review PDF

Full Text: DOI

References:

[1]	Björck, Å., Solving linear least squares problems by Gram-Schmidt orthogonalization, BIT, 7, 1-21 (1967) · Zbl 0183.17802
[2]	Björck, Å., Iterative refinement of linear least squares solutions,part 2, BIT, 8, 8-30 (1968) · Zbl 0177.43204
[3]	Daniel, J. W.; Gragg, W. B.; Kaufman, L.; Stewart, G. W., Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization, Math. Comp., 30, 772-795 (1976) · Zbl 0345.65021
[4]	T. Ericsson, An analysis of orthogonalization in elliptic norms, to appear.; T. Ericsson, An analysis of orthogonalization in elliptic norms, to appear.
[5]	Ericsson, T.; Ruhe, A., The spectral transformation Lanczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems, Math. Comp., 35, 1251-1268 (1980) · Zbl 0468.65021
[6]	Gander, W., Algorithms for the QR decomposition, (Res. Rep. 80-02, Sem. Angew. Math. (1980), ETH: ETH Zurich) · Zbl 0366.65012
[7]	Golub, G. H., Numerical methods for solving linear least squares problems, Numer. Math., 7, 206-216 (1965) · Zbl 0142.11502
[8]	Golub, G. H.; Underwood, R.; Willdnson, J. H., The Lanczos algorithm for the symmetric Ax = λBx problem, (Tech. Rep. STAN-CS-72-270, (1972), Computer Science Dept., Stanford Univ)
[9]	Dongarra, J. J.; Moler, C. B.; Bunch, J. R.; Stewart, G. W., (Linpack Users Guide (1979), SIAM: SIAM Philadelphia)
[10]	Paige, C. C.; Saunders, M., Alg 583 LSQR,, ACM Trans. Math. Software, 8, 195-201 (1982)
[11]	Ruhe, A., The two-sided Arnoldi algorithm for nonsymmetric eigenvalue problems, (Proceedings of the Conference on Matrix Pencils. Proceedings of the Conference on Matrix Pencils, Piteå (1982), Springer LNM), to appear · Zbl 0502.65022
[12]	Saad, Y., Variations on Arnoldi’s method for computing eigenelements of large unsymmetric matrices, Linear Algebra Appl., 34, 269-295 (1980) · Zbl 0456.65017
[13]	Saad, Y., The Lanczos biorthogonalization algorithm and other oblique projection methods for solving large unsymmetric systems, SIAM J. Numer. Anal., 19, 485-506 (1982) · Zbl 0483.65022
[14]	Saad, Y., Projection methods for solving large sparse eigenvalue problems, (Proceedings of the Conference on Matrix Pencils. Proceedings of the Conference on Matrix Pencils, Piteå (1982), Springer LNM), to appear · Zbl 0501.65014
[15]	Schwarz, H. R.; Rutishauser, H.; Stiefel, E., Matrizen-Numerik (1968), Teubner · Zbl 0174.46701
[16]	Varga, R. S., Matrix Iterative Analysis (1962), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J · Zbl 0133.08602

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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.