Efficient computation of the matrix cosine

Trigonometric matrix functions play a fundamental role in second order differential equation systems. This work presents an algorithm for computing the cosine matrix function based on Taylor series and the cosine double angle formula. It uses a forward absolute error analysis providing sharper bounds than existing methods. The proposed algorithm had lower cost than state-of-the-art algorithms based on Hermite matrix polynomial series and Padé approximants with higher accuracy in the majority of test matrices.

► A new algorithm for matrix cosine computation is proposed.
► It uses Taylor expansion and the double angle formula with sharp truncation error bounds.
► A Matlab implementation is provided: costay.m.
► In tests it was more accurate than state-of-the-art algorithms with a lower cost (8–17%).