The Fast Generalized Parker-Traub Algorithm for Inversion of Vandermonde and Related Matrices
The Fast Generalized Parker-Traub Algorithm for Inversion of Vandermonde and Related Matrices
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DOI：
10.1006/jcom.1997.0442
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发表时间：
1997-06
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影响因子：
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通讯作者：
I. Gohberg;V. Olshevsky
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文献类型：
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作者：
I. Gohberg;V. Olshevsky
In this paper we compare the numerical properties of the well-knownfastO(n2) Traub and Bjorck?Pereyra algorithms, which both use the special structure of a Vandermonde matrix to rapidly compute the entries of its inverse. The results of numerical experiments suggest that the Parker variant of what we shall call the Parker?Traub algorithm allows one not onlyfastO(n2) inversion of a Vandermonde matrix, but it also gives moreaccuracy. We also show that the Parker?Traub algorithm is connected to the well-known concept ofdisplacement rank,introduced by Kailath, Kung, and Morf about two decades ago, and therefore this algorithm can be generalized to invert the more general class ofVandermonde-likematrices, naturally suggested by the idea of displacement.
