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矩阵指数精细积分方法中参数的自适应选择

Adaptive selection of parameters for precise computation of matrix exponential based on padé approximation

  • 摘要: 讨论了基于Pad\'e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N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.

     

    Abstract: Adaptive selection is discussed for scaling parametersN and expanded series q in precise integration method (PIM) of matrixexponential based on Pad\'e approximation. In general, scaling parametersN and expanded series q play important roles in the numerical accuracyand computational efficiency of matrix exponential. Using theapproximation theory of matrix functions, influences of parameters N andq on the computational accuracy and efficiency are firstly studied, andthen the iterative adaptive selection algorithm for optimal combination ofparameters (N,q) is presented. Appropriate parameters (N,q) can beselected automatically depending on the characteristics of the matrix, andthe computation amount of adaptive selection can be neglected compared withthat of matrix exponential. So it is very important for enhancing theadaptations and increasing the computation efficiencies of matrixexponential. In addition, computational examples are carried out to testifythe correctness and validity of the present method.

     

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