Computing the matrix sine and cosine simultaneously with a reduced number of products

10/01/2020

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by   Muaz Seydaoglu, et al.

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A new procedure is presented for computing the matrix cosine and sine simultaneously by means of Taylor polynomial approximations. These are factorized so as to reduce the number of matrix products involved. Two versions are developed to be used in single and double precision arithmetic. The resulting algorithms are more efficient than schemes based on Padé approximations for a wide range of norm matrices.