Bounds for variable degree rational L∞ approximations to the matrix cosine

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 and we present intervals of applications for rational L∞ approximations of various degrees for these types of matrices in the lines of [3]. Our method relies on Remez algorithm for rational approximation while the innovation here is the choice of the starting set of non-symmetrical Chebyshev points. Only one Remez iteration is then enough to quickly approach infinitesimally close to the required L∞ approximant.