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2013 A New Algorithm to Approximate Bivariate Matrix Function via Newton-Thiele Type Formula
Rongrong Cui, Chuanqing Gu
J. Appl. Math. 2013: 1-10 (2013). DOI: 10.1155/2013/642818

Abstract

A new method for computing the approximation of bivariate matrix function is introduced. It uses the construction of bivariate Newton-Thiele type matrix rational interpolants on a rectangular grid. The rational interpolant is of the form motivated by Tan and Fang (2000), which is combined by Newton interpolant and branched continued fractions, with scalar denominator. The matrix quotients are based on the generalized inverse for a matrix which is introduced by C. Gu the author of this paper, and it is effective in continued fraction interpolation. The algorithm and some other important conclusions such as divisibility and characterization are given. In the end, two examples are also given to show the effectiveness of the algorithm. The numerical results of the second example show that the algorithm of this paper is better than the method of Thieletype matrix-valued rational interpolant in Gu (1997).

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Rongrong Cui. Chuanqing Gu. "A New Algorithm to Approximate Bivariate Matrix Function via Newton-Thiele Type Formula." J. Appl. Math. 2013 1 - 10, 2013. https://doi.org/10.1155/2013/642818

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1266.65015
MathSciNet: MR3033567
Digital Object Identifier: 10.1155/2013/642818

Rights: Copyright © 2013 Hindawi

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