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

Computing a function f(A)f(A) of an nn-by-nn matrix AA 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)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 AA. 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.