Positive cones and convergence conditions for iterative methods based on splittings

作     者：Climent, JJ Herranz, V Perea, C 

作者机构：Univ Alicante Dept Ciencia Comput & Intelligencia Artificial E-03080 Alicante Spain Univ Miguel Hernandez Dept Estadist & Matemat Aplicada Ctr Invest Operat E-03202 Elche Spain Univ Miguel Hernandez Dept Estadist & Matemat Aplicada Ctr Invest Operat EPSO E-03312 Orihuela Spain 

出 版 物：《LINEAR ALGEBRA AND ITS APPLICATIONS》 (线性代数及其应用)

年 卷 期：2006年第413卷第2-3期

页      面：319-326页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：linear system positivity cone partial order splitting convergence result 

摘      要：The study of convergence conditions to solve large and sparse linear systems Ax = b by iterative methods has been discussed by many authors. In this paper, by using the partial order induced by positivity cone of matrices and conditions on the matrices and splittings, we obtain the convergence of the iterative method. The usual partial orders of nonnegative matrices and nonnegative definite matrices satisfy the conditions presented for this new order, and hence, we unify the theory. Moreover, we also show that the new conditions apply to other partial orders as well, thus extending the usual convergence theory to a new situation. (c) 2005 Elsevier Inc. All rights reserved.