×

zbMATH — the first resource for mathematics

Perturbation bounds for the definite generalized eigenvalue problem. (English) Zbl 0407.15012

MSC:
15A18 Eigenvalues, singular values, and eigenvectors
15B57 Hermitian, skew-Hermitian, and related matrices
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Brickman, L., On the fields of values of a matrix, Proc. amer. math. soc., 12, 61-66, (1961) · Zbl 0104.01204
[2] Calabi, E., Linear systems of real quadratic forms, Proc. amer. math. soc., 15, 844-846, (1964) · Zbl 0178.35903
[3] Crawford, C.R., A stable generalized eigenvalue problem, SIAM J. numer. anal., 6, 854-860, (1976) · Zbl 0348.15005
[4] Davis, C.; Kahan, W., The rotation of eigenvectors by a pertubation, SIAM J. numer. anal., 7, 1-46, (1970) · Zbl 0198.47201
[5] Greub, W.H., Linear algebra, (1967), Springer New York · Zbl 0147.27408
[6] Hestenes, M.R., Pairs of quadratic forms, Linear algebra and appl., 1, 397-407, (1968) · Zbl 0174.06401
[7] Householder, A.S., The theory of matrices in numerical analysis, (1964), Blaisdel New York · Zbl 0161.12101
[8] Kato, T., Pertubation theory for linear operators, (1966), Springer New York
[9] Stewart, G.W., Error bounds for approximate invariant subspaces of closed linear operators, SIAM J. numer. anal., 8, 796-808, (1971) · Zbl 0232.47010
[10] Stewart, G.W., On the sensitivity of the eigenvalue problem ax = λbx, SIAM J. numer. anal., 9, 669-686, (1972) · Zbl 0252.65026
[11] Stewart, G.W., Error and pertubation bounds for subspaces associated with certain eigenvalue problems, SIAM rev., 15, 764-772, (1973) · Zbl 0297.65030
[12] Stewart, G.W., Gershgorin theory for the generalized eigenvalue problem ax = λbx, Math. comp., 29, 600-606, (1975) · Zbl 0302.65028
[13] G.W. Stewart, On the pertubation of pseudo-inverses, projections, and linear least squares problems, SIAM Rev. to be published.
[14] Taussky, O., Positive definite matrices, (), 309-319
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.