三对角线块Toeplitz线性系统的GMRES

Pub Date : 2018-12-30 DOI:10.3336/GM.53.2.12

R. Doostaki, Young Researchers

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引用次数: 0

摘要

研究了求解具有m × m对角块的三对角块Toeplitz线性方程组Ax = b的广义最小残差(GMRES)方法。当m = 1时，这些系统成为三对角Toeplitz线性系统，当m > 1时，A成为m-三对角Toeplitz矩阵。我们的第一个主要目标是找到b = (B1, 0，…)时GMRES残差的精确表达式。， 0)， b =(0，…， 0, BN) T，其中B1和BN是m向量。建立了GMRES残差的上界和下界来解释数值行为。三对角线块Toeplitz线性系统的GMRES残差上界已在文献[1]中进行了研究。此外，本文还考虑了正规的三对角线块Toeplitz线性系统。第二个主要目标是找到这些系统的GMRES残差的下界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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GMRES on tridiagonal block Toeplitz linear systems

We study the generalized minimal residual (GMRES) method for solving tridiagonal block Toeplitz linear system Ax = b with m × m diagonal blocks. For m = 1, these systems becomes tridiagonal Toeplitz linear systems, and for m > 1, A becomes an m-tridiagonal Toeplitz matrix. Our first main goal is to find the exact expressions for the GMRES residuals for b = (B1, 0, . . . , 0) , b = (0, . . . , 0, BN ) T , where B1 and BN are m-vectors. The upper and lower bounds for the GMRES residuals were established to explain numerical behavior. The upper bounds for the GMRES residuals on tridiagonal block Toeplitz linear systems has been studied previously in [1]. Also, in this paper, we consider the normal tridiagonal block Toeplitz linear systems. The second main goal is to find the lower bounds for the GMRES residuals for these systems.

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