论文标题
关于Sassenfeld标准及其与H-矩阵的联系
A note on the Sassenfeld criterion and its relation to H-matrices
论文作者
论文摘要
本说明的起点是1951年Sassenfeld在经典高斯 - 塞德尔法的收敛中，由Sassenfeld在1951年提出的一个数十年却鲜为人知的足够条件。本文的目的是为Sassenfeld的标准提供新的启示，并证明它与H-膜直接相关。特别是，我们的结果产生了H-膜的新表征。此外，简要讨论了涉及H-矩阵预调节器的迭代线性求解器的收敛性。
The starting point of this note is a decades-old yet little-noticed sufficient condition, presented by Sassenfeld in 1951, for the convergence of the classical Gauss-Seidel method. The purpose of the present paper is to shed new light on Sassenfeld's criterion and to demonstrate that it is directly related to H-matrices. In particular, our results yield a new characterization of H-matrices. In addition, the convergence of iterative linear solvers that involve H-matrix preconditioners is briefly discussed.
