Realistic error bounds for a simple eigenvalue and its associated eigenvector |
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Authors: | H J Symm J H Wilkinson |
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Institution: | (1) Division of Numerical Analysis and Computer Science, National Physical Laboratory, Teddington, Middlesex, England;(2) Department of Computer Science, Stanford University, 94305 Stanford, California, USA |
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Abstract: | Summary An algorithm is described which, given an approximate simple eigenvalue and a corresponding approximate eigenvector, provides rigorous error bounds for improved versions of them. No information is required on the rest of the eigenvalues, which may indeed correspond to non-linear elementary divisors. A second algorithm is described which gives more accurate improved versions than the first but provides only error estimates rather than rigorous bounds. Both algorithms extend immediately to the generalized eigenvalue problem.Dedicated to A.S. Householder on his 75th birthday |
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Keywords: | AMS (MOS): 65F15 CR: 5 14 |
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