Computing matrix functions using mixed interpolation methods

Computing matrix functions plays a diverse role in science and engineering. By applying mixed interpolation methods with arbitrary nodes for approximating real functions and the eigenvalues of the given matrix A , we propose a definition for computing the matrix function f ( A ) . We will show the existence and uniqueness of the proposed definition. By using this definition, we present various practical techniques for computing the matrix function f ( A ) . Finally some numerical examples and an application are given to show the applicability and the efficiency of the presented techniques.