矩阵指数精细积分方法中参数的自适应选择

摘要

Adaptive selection is discussed for scaling parameters N and expanded series q in precise inte-gration method (PIM) of matrix exponential based on Padé approximation. In general, scaling parameters N and expanded series q play important roles in the numerical accuracy and computational efficiency of matrix exponential. Using the approximation theory of matrix functions, influences of parameters N and q on the computational accuracy and efficiency are firstly studied, and then the iterative adaptive selection algorithm for optimal combination of parameters (N, q) is presented. Appropriate parameters (N, q) can be selected automat-ically depending on the characteristics of the matrix, and the computation amount of adaptive selection can be neglected compared with that of matrix exponential. So it is very important for enhancing the adaptations and increasing the computation efficiencies of matrix exponential. In addition, computational examples are carried out to testify the correctness and validity of the present method.%讨论了基于Pad逼近的矩阵指数精细积分方法中加权系数N和展开项数q的自适应选择问题.参数(N,q)的选择直接影响到矩阵指数计算的精度和效率.采用矩阵函数逼近理论,研究了参数Ⅳ和q的增加对精度的影响程度,据此,提出了参数(N,q)优化组合的递推自适应选择方法.该方法可以根据矩阵本身的性态选择合适的参数(N,q),而参数选择的计算量与矩阵指数的计算量相比几乎可以忽略,这对于增强矩阵指数精细积分方法的适应性和提高计算效率是很有益处的.算例验证了该方法的正确性和有效性.