Minimax vs Pade approximation of matrix exponential for normal and nonnegative matrices

The most widely studied matrix function is the matrix exponential, mainly because of its key role in the solution of differential equations. In this work we derive new alternatives for efficient computation of the matrix cosine. We focus especially on the two classes of Normal and Nonnegative matrices for which we study the interval of application for rational [7/7] L∞ approximation compared to the corresponding [7/7] Pade approximant when we implement the scaling and squaring Algorinthm [2].