基于Taylor级数的矩阵双曲余弦函数的数值算法

Numerical Algorithm of Matrix Hyperbolic Cosine Function Based on Taylor Series

提出了一种基于Taylor级数的矩阵双曲余弦函数的数值逼近算法,为减少计算量使用了Paterson-Stockmeyer方法来计算矩阵Taylor多项式,对逼近误差进行了绝对后向误差分析以减少误差,并设计了算法可以较为快速且准确地求解矩阵双曲余弦函数,最后进行了数值实验,验证了算法的有效性.

A numerical approximation algorithm for matrix hyperbolic cosine functions based on Taylor series is proposed.The Paterson-Stockmeyer method is used to reduce the computational complexity to calculate the matrix Taylor polynomial,and the absolute backwarderror analysis of the approximation error is performed to reduce the error.The algorithm is designed to solve the matrix hyperbolic cosine function quickly and accurately.Finally,numerical experiments are carried out to verify the effectiveness of the algorithm.