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On the convergence theory of double K-weak splittings of type II

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 convergenc...

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Detalles Bibliográficos
Autores principales: Shekhar, Vaibhav, Mishra, Nachiketa, Mishra, Debasisha
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8457540/
https://www.ncbi.nlm.nih.gov/pubmed/34580564
http://dx.doi.org/10.21136/AM.2021.0270-20
Descripción
Sumario: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 [Formula: see text] . The convergence behavior is discussed by performing numerical experiments for different matrices derived from the discretized Poisson equation.