Practical methods for evaluating the accuracy of the eigenelements of a symmetric matrix

Faezeh Toutounian

Mathematics and Computers in Simulation (MATCOM), 1988, vol. 30, issue 6, 493-504

Abstract: The results of the Householder and QL algorithms for determining the eigenelements of a symmetric matrix, provided by a computer, always contain the errors resulting from floating-point arithmetic round-off error propagation. The Permutation-Perturbation method is a very efficient practical method for evaluating these errors and consequently for estimating the exact significant figures of the eigenelements. But, in the cases of: eigenvalues very close to zero, eigenvalues of widely varying range, and multiple eigenvalues, the Permutation-Perturbation method is not complete. In this paper we propose an algorithm which is able to complete this method.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:30:y:1988:i:6:p:493-504

DOI: 10.1016/0378-4754(88)90071-7

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