ITERATIVE COMPUTING THE MINIMAL SOLUTION OF THE COUPLED NONLINEAR MATRIX EQUATIONS IN TERMS OF NONNEGATIVE MATRICES

Q4 Mathematics

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 1900-01-01 DOI:10.56082/annalsarscimath.2020.1-2.226

I. Ivanov

引用次数: 1

Abstract

We investigate a set of nonlinear matrix equations with nonnegative matrix coefficients which has arisen in applied sciences. There are papers where the minimal nonnegative solution of the set of nonlinear matrix equations is computed applying the different procedures. The alternate linear implicit method and its modifications have intensively investigated because they have simple computational scheme. We construct a new decoupled modification of the alternate linear implicit procedure to compute the minimal nonnegative solution of the considered set of equations. The convergence properties of the proposed iteration are derived and a sufficient condition for convergence is derived. The performance of the proposed algorithm is illustrated on several numerical examples. On the basis of the experiments we derive conclusions for applicability of the computational schemes.

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用非负矩阵形式迭代计算耦合非线性矩阵方程的最小解

研究了应用科学中出现的一组非负矩阵系数的非线性矩阵方程。有论文用不同的方法计算了非线性矩阵方程组的最小非负解。交替线性隐式方法及其修正由于其计算格式简单而得到了广泛的研究。我们构造了一种新的解耦的交替线性隐式过程来计算所考虑的方程组的最小非负解。推导了该迭代算法的收敛性，并给出了收敛的充分条件。数值算例说明了该算法的性能。在实验的基础上，得出了计算格式的适用性结论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Mathematics-Mathematics (all)

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

25 weeks

期刊介绍： The journal Mathematics and Its Applications is part of the Annals of the Academy of Romanian Scientists (ARS), in which several series are published. Although the Academy is almost one century old, due to the historical conditions after WW2 in Eastern Europe, it is just starting with 2006 that the Annals are published. The Editor-in-Chief of the Annals is the President of ARS, Prof. Dr. V. Candea and Academician A.E. Sandulescu (†) is his deputy for this domain. Mathematics and Its Applications invites publication of contributed papers, short notes, survey articles and reviews, with a novel and correct content, in any area of mathematics and its applications. Short notes are published with priority on the recommendation of one of the members of the Editorial Board and should be 3-6 pages long. They may not include proofs, but supplementary materials supporting all the statements are required and will be archivated. The authors are encouraged to publish the extended version of the short note, elsewhere. All received articles will be submitted to a blind peer review process. Mathematics and Its Applications has an Open Access policy: all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. No submission or processing fees are required. Targeted topics include : Ordinary and partial differential equations Optimization, optimal control and design Numerical Analysis and scientific computing Algebraic, topological and differential structures Probability and statistics Algebraic and differential geometry Mathematical modelling in mechanics and engineering sciences Mathematical economy and game theory Mathematical physics and applications.