A Piecewise Modified Matrix Padé-type Approximation of Hybrid Order in the Interval [0, 1]

Abstract

In this paper, we introduce a piecewise modified matrix Pad\u00e9-type approximation of hybrid order in the interval [0, 1]. It yields highly accurate results and exact values at some given points. The accuracy of this approximation increases as the order or the node increases. This method can be applied to approximate the exponential function. The explicit formula for computing the matrix exponential is presented. A numerical example is given to illustrate the effectiveness of this method.