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

โœ Scribed by Faezeh Toutounian

Publisher
Elsevier Science
Year
1988
Tongue
English
Weight
761 KB
Volume
30
Category
Article
ISSN
0378-4754

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โœฆ Synopsis

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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โœ Xingping Sheng; Guoliang Chen ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 676 KB

In this paper, two efficient iterative methods are presented to solve the symmetric and skew symmetric solutions of a linear matrix equation AXB + CYD = E, respectively, with real pair matrices X and Y . By these two iterative methods, the solvability of the symmetric and skew symmetric solutions fo