Journal of Applied Mathematics

A New Algorithm to Approximate Bivariate Matrix Function via Newton-Thiele Type Formula

Rongrong Cui and Chuanqing Gu

Full-text: Open access

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).

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 642818, 10 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394807876

Digital Object Identifier
doi:10.1155/2013/642818

Mathematical Reviews number (MathSciNet)
MR3033567

Zentralblatt MATH identifier
1266.65015

Citation

Cui, Rongrong; Gu, Chuanqing. A New Algorithm to Approximate Bivariate Matrix Function via Newton-Thiele Type Formula. J. Appl. Math. 2013 (2013), Article ID 642818, 10 pages. doi:10.1155/2013/642818. https://projecteuclid.org/euclid.jam/1394807876


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