Open AccessOn the convergence theory of double $K$-weak splittings of type II
Author(s) -
Vaibhav Shekhar,
Nachiketa Mishra,
Debasisha Mishra
Publication year - 2021
Publication title -
pubmed central
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.237
H-Index - 28
eISSN - 1572-9109
pISSN - 0862-7940
DOI - 10.21136/am.2021.0270-20
Subject(s) - mathematics , convergence (economics) , monotone polygon , discretization , type (biology) , invariant (physics) , matrix (chemical analysis) , combinatorics , mathematical analysis , pure mathematics , discrete mathematics , mathematical physics , geometry , ecology , materials science , composite material , economics , biology , economic growth
Recently, Wang (2017) has introduced the K -nonnegative double splitting using the notion of matrices that leave a cone K ⊆ 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.