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Bounds for relative errors of complex matrix factorizations

โœ Scribed by A. Largillier

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
405 KB
Volume
9
Category
Article
ISSN
0893-9659

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Many problems in applied mathematics require the evaluation of matrix functionals of the form F(A):= uTf(A)u, where A is a large symmetric matrix and u is a vector. Golub and collaborators have described how approximations of such functionals can be computed inexpensively by using the Lanczos algori

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An error bound for approximate eigenvalues of a complex n-dimensional pencil (A, B) is given. From our theorem several well-known bounds follow as corollaries. Our result takes into account the general residual AX -BXW, where X ~ C n x m and W ~ C mxm with m ~< n.