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

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.