On the Convergence Theory of Double K-Weak Splittings of Type II

被引：0

作者：

Shekhar, Vaibhav ^{[1
]}

Mishra, Nachiketa ^{[2
]}

Mishra, Debasisha ^{[1
]}

机构：

[1] Natl Inst Technol, Dept Math, Great Eastern Rd, Raipur, Madhya Pradesh, India

[2] Indian Inst Informat Technol Design & Mfg, Dept Math, Kancheepuram 600127, India

来源：

APPLICATIONS OF MATHEMATICS | 2022年 / 67卷 / 03期

关键词：

linear system; iterative method; K-nonnegativity; double splitting; convergence theorem; comparison theorem;

D O I：

10.21136/AM.2021.0270-20

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Recently,Wang (2017) has introduced the K-nonnegative double splitting using the notion of matrices that leave a cone K subset of R-n invariant and studied its convergence theory by generalizing the corresponding results for the nonnegative double splitting by Song and Song (2011). However, the convergence theory for K -weak regular and K -nonnegative double splittings of type II is not yet studied. In this article, we first introduce this class of splittings and then discuss the convergence theory for these sub-classes of matrices. We then obtain the comparison results for two double splittings of a K -monotone matrix. Most of these results are completely new even for K = R-+(n). The convergence behavior is discussed by performing numerical experiments for different matrices derived from the discretized Poisson equation.

引用

页码：341 / 369

页数：29

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