an:04056891
Zbl 0647.65031
Qiao, Jiyue
Error analysis and determination of the scaling constant for the scaling power method
ZH
Acta Math. Appl. Sin. 10, No. 4, 491-497 (1987).
00152781
1987
j
65F30 65L05
scaling power method; matrix exponential; skip product method; error analysis; numerical example; ill-conditioned differential equation
The scaling power method discussed intensively by \textit{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.
Wang Chengshu
Zbl 0363.65031