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

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  • Toutounian, Faezeh

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.

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  • Toutounian, Faezeh, 1988. "Practical methods for evaluating the accuracy of the eigenelements of a symmetric matrix," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 493-504.
    • Handle: RePEc:eee:matcom:v:30:y:1988:i:6:p:493-504
    DOI: 10.1016/0378-4754(88)90071-7
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    References listed on IDEAS

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    1. Vignes, J., 1978. "New methods for evaluating the validity of the results of mathematical computations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 20(4), pages 227-249.
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