Determination of a matrix function using the divided difference method of Newton and the interpolation technique of Hermite

Authors:
Mehdi Dehghan;Masoud Hajarian
Affiliations:
Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran 15914, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran 15914, Iran
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

Computing a function f(A) of an n-by-n matrix A is a frequently occurring problem in control theory and other applications. In this paper we introduce an effective approach for the determination of matrix function f(A). We propose a new technique which is based on the extension of Newton divided difference and the interpolation technique of Hermite and using the eigenvalues of the given matrix A. The new algorithm is tested on several problems to show the efficiency of the presented method. Finally, the application of this method in control theory is highlighted.