Improving Jacobi methods for nonnegative \(H\)-matrices linear systems
The authors generalize results of \textit{Y. Zhang, T.-Z. Huang} and \textit{X.-P. Liu} [Comput.\ Math.\ Appl. 50, No.~10--12, 1587--1602 (2005; Zbl 1087.65031)] for linear systems whose matrix is a nonnegative \(H\)-matrix. The main idea is to construct a preconditioner \(P\) for the Jacobi method. This \(P\) takes the form of the identity matrix with one nonzero off-diagonal element per row. The position and the value of these off-diagonal elements are chosen so as to optimize the convergence, i.e., to minimize the spectral radius of the iteration matrix.
scientific article; zbMATH DE number 5162010