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.

中文翻译：

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同时计算矩阵正弦和余弦并减少乘积

提出了一种新的过程，用于通过泰勒多项式逼近同时计算矩阵余弦和正弦。将这些因素分解以减少涉及的基质产物的数量。开发了两种版本以用于单精度和双精度算术。对于广泛的范数矩阵，所得算法比基于Padé逼近的方案更有效。