The Tensor Pade´-Type Approximant with Application in Computing Tensor Exponential Function

Tensor exponential function is an important function that is widely used. In this paper, tensor Pade´-type approximant (TPTA) is defined by introducing a generalized linear functional for the first time. The expression of TPTA is provided with the generating function form. Moreover, by means of formal orthogonal polynomials, we propose an efficient algorithm for computing TPTA. As an application, the TPTA for computing the tensor exponential function is presented. Numerical examples are given to demonstrate the efficiency of the proposed algorithm.