求解自反和反自反矩阵上耦合矩阵方程的两种迭代算法

IF 2.5 3区数学 Q1 MATHEMATICS, APPLIED

Computational & Applied Mathematics Pub Date : 2012-08-28 DOI:10.1590/S1807-03022012000200008

M. Dehghan, M. Hajarian

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引用次数: 17

摘要

如果PT = P且P2 = I(其中PT为P的转置)，则称n×n实矩阵P为广义反射矩阵。如果a = P a P (a = - P a P)，则称矩阵a∈Rn×n为广义反射矩阵P的自反(反)矩阵。自反矩阵和反自反矩阵在许多领域都有广泛的应用。本文提出了求解耦合矩阵方程{A1 XB1 + C1XTD1 = M1的两种迭代算法。a2xb2 + c2xtd2 = m2。分别在自反矩阵和反自反矩阵上。证明了对于任意初始自反(反)矩阵，第一(第二)算法收敛于耦合矩阵方程的自反(反)解。最后用两个数值算例说明了所提算法的有效性。数学学科分类:15A06、15A24、65F15、65F20。

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Two iterative algorithms for solving coupled matrix equations over reflexive and anti-reflexive matrices

An n × n real matrix P is said to be a generalized reflection matrix if PT = P and P2 = I (where PT is the transpose of P). A matrix A ∈ Rn×n is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A = P A P (A = - P A P). The reflexive and anti-reflexive matrices have wide applications in many fields. In this article, two iterative algorithms are proposed to solve the coupled matrix equations { A1 XB1 + C1XTD1 = M1. A2 XB2 + C2XTD2 = M2. over reflexive and anti-reflexive matrices, respectively. We prove that the first (second) algorithm converges to the reflexive (anti-reflexive) solution of the coupled matrix equations for any initial reflexive (anti-reflexive) matrix. Finally two numerical examples are used to illustrate the efficiency of the proposed algorithms. Mathematical subject classification: 15A06, 15A24, 65F15, 65F20.

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来源期刊

Computational & Applied Mathematics Mathematics-Computational Mathematics

CiteScore

4.50

自引率

11.50%

发文量

352

审稿时长

>12 weeks

期刊介绍： Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics). The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.