## Journal of Applied Mathematics

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

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

#### 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