An Algorithm for Computing the Matrix Cosine
Steven M. Serbin, Sybil A. Blalock · SIAM Journal on Scientific and Statistical Computing · 1980
We present and analyze an algorithm for computing the cosine of a matrix which is based on the double-angle formula $\cos 2A = 2\cos ^2 A - I$. We discuss the relevance of this computation to second-order matrix differential equations. We draw the analogy between this method for the cosine and the familiar scaling and squaring method for computing the matrix exponential. Numerical experiments employing polynomial and rational approximations to the cosine, in conjunction with the double angle technique, are presented.