Journal of Applied Mathematics
Volume 2013 (2013), Article ID 642818, 10 pages
Research Article

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

1Department of Mathematics, Shanghai University, Shanghai 200444, China
2School of Mathematical Science, Yancheng Teachers University, Yancheng 224000, China

Received 22 October 2012; Revised 6 December 2012; Accepted 10 December 2012

Academic Editor: Juan Manuel Peña

Copyright © 2013 Rongrong Cui and Chuanqing Gu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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).