摘要
对矩阵指数运算的PSSA方法与精细积分方法 (PIM )在实际应用中的最佳运算量等问题进行了讨论 .可以发现 ,在一般情况下PSSA方法有较小的计算量 ,但其存在矩阵求逆问题 ;PIM方法则具有无需矩阵求逆的特点 ,且算法由计算机位数限制造成的截断误差较PSSA方法的低 .进一步对PIM算法在 2 N 运算中N值的选取与展开项数的选取提出了改进建议 。
This paper gives a discussion about the computational cost and some other problems when the two numerical methods, i.e. Pade scaling and squaring approximation (PSSA), precise integration method (PIM), are used in the computation of the matrix exponential. It can be found that, in general, the PSSA has less computing time than PIM, but need an inverse computation of a matrix which will not exist in the PIM. Also, the roundoff error induced by computer in the PIM is smaller than that exists in the PSSA. Furthermore, the improvement for both the selection of parameter N and the item number in the Taylor series expansion for the 2 N computation algorithm of PIM is given in this paper, which is rather important for the computation of the matrix exponential.
出处
《大连理工大学学报》
CAS
CSCD
北大核心
2000年第5期522-525,共4页
Journal of Dalian University of Technology
基金
国家自然科学基金!资助项目 ( 1973 2 0 2 0 )
国家重点基础研究专项经费资助项目 !(G19990 3 2 80 5 )
关键词
矩阵
矩阵函数
数值计算
指数运算
matrix
matrix function
numerical computation/Pade approximation
precise integration
