On optimal improvements of classical iterative schemes for Z-matrices
On optimal improvements of classical iterative schemes for Z-matrices
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DOI：
10.1016/j.cam.2005.03.057
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发表时间：
2006-04
影响因子：
2.4
通讯作者：
D. Noutsos;M. Tzoumas
中科院分区：
文献类型：
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作者：
D. Noutsos;M. Tzoumas
许多研究人员考虑了应用于线性系统的预条件子，其矩阵系数是 Z 或 M 矩阵，使得相关的雅可比和高斯-赛德尔方法比未预条件的方法渐近收敛得更快。选择这样的预处理器是为了消除同一列的非对角元素或第一个上对角线的元素 [Milaszewicz, LAA 93 (1987) 161–170]，Gunawardena 等人。 [LAA 154–156 (1991) 123–143]。在这项工作中，我们概括了以前的预处理器以获得最佳方法。给出了“好”雅可比和高斯-赛德尔算法，并提出并分析了每行消除多个条目的预处理器。此外，还研究了上述预处理器对 Krylov 子空间方法的行为。
Many researchers have considered preconditioners, applied to linear systems, whose matrix coefficient is a Z- or an M-matrix, that make the associated Jacobi and Gauss–Seidel methods converge asymptotically faster than the unpreconditioned ones. Such preconditioners are chosen so that they eliminate the off-diagonal elements of the same column or the elements of the first upper diagonal [Milaszewicz, LAA 93 (1987) 161–170], Gunawardena et al. [LAA 154–156 (1991) 123–143]. In this work we generalize the previous preconditioners to obtain optimal methods. “Good” Jacobi and Gauss–Seidel algorithms are given and preconditioners, that eliminate more than one entry per row, are also proposed and analyzed. Moreover, the behavior of the above preconditioners to the Krylov subspace methods is studied.