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Error analysis and determination of the scaling constant for the scaling power method. (Chinese) Zbl 0647.65031
The scaling power method discussed intensively by R. C. Ward [SIAM J. numer. Anal. 14, 600-610 (1977; Zbl 0363.65031)] is one of the most efficient methods for computing the matrix exponential \(e^{At}\) which is implemented through converting \(e^{At}\) into \([e^{At/N}]^ N\). In this paper, an appropriate choosen interval for N is given. A skip product method to overcome the difficulty of huge amount of computation and the error analysis of the method are advanced. A numerical example of an ill-conditioned differential equation with the rigidity ratio \(10^ 6\) is included.
Reviewer: Wang Chengshu
65F30 Other matrix algorithms (MSC2010)
65L05 Numerical methods for initial value problems involving ordinary differential equations