In this paper, we introduce a new piecewise rational interpolation based on matrix Pade-type approximation, that is, a piecewise matrix Pade-type approximation of hybrid order in the interval
It yields more accurate results and exact values at some given points. This method can be applied to approximate the exponential function. The explicit formula for computing the matrix exponential is presented. It is shown by a numerical example that the accuracy of the approximation increases as the order or the node increases.
