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 AA, we propose a definition for computing the matrix function f(A)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)f(A). Finally some numerical examples and an application are given to show the applicability and the efficiency of the presented techniques.