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The Accurate Inversion of Vandermonde Matrices

Jog, CS (2004) The Accurate Inversion of Vandermonde Matrices. In: Computers & Mathematics with Applications, 47 (6-7). pp. 921-929.

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Two modifications are suggested in the commonly used algorithms (such as the $O(n^2)$ Parker algorithm) for the explicit inversion of Vandermonde matrices resulting in an algorithm whose accuracy is no worse than those of the existing algorithms, but which is significantly more accurate in many pathological situations. The first modification circumvents, to some extent, the subtraction of ‘two big like-signed numbers’ which in turn reduces round-off errors, while the second modification exploits the structure of the inverse and uses two recursive formulae instead of one to bring about an increase in accuracy. Numerical results are presented to demonstrate the increase in accuracy that results from these two modifications. Although the modified algorithm is always at least as accurate as the Parker algorithm, it does, unfortunately, involve an increase in complexity from $O(n^2)$ to $O(n^3)$, so that use of this algorithm to increase the relative accuracy is recommended only in situations where the standard algorithms fail to yield accurate results.

Item Type: Journal Article
Publication: Computers & Mathematics with Applications
Publisher: Elsevier
Additional Information: Copyright of this article belongs to Elsevier.
Keywords: Accurate Vandermonde inverse
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Date Deposited: 18 Oct 2006
Last Modified: 19 Sep 2010 04:32
URI: http://eprints.iisc.ac.in/id/eprint/8723

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