Article
| Title: | On the convergence theory of double $K$-weak splittings of type II (English) |
| Author: | Shekhar, Vaibhav |
| Author: | Mishra, Nachiketa |
| Author: | Mishra, Debasisha |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 67 |
| Issue: | 3 |
| Year: | 2022 |
| Pages: | 341-369 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Recently, Wang (2017) has introduced the $K$-nonnegative double splitting using the notion of matrices that leave a cone $K\subseteq \mathbb {R}^{n}$ 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 $K= \mathbb {R}^{n}_+$. The convergence behavior is discussed by performing numerical experiments for different matrices derived from the discretized Poisson equation. (English) |
| Keyword: | linear system |
| Keyword: | iterative method |
| Keyword: | $K$-nonnegativity |
| Keyword: | double splitting |
| Keyword: | convergence theorem |
| Keyword: | comparison theorem |
| MSC: | 15A06 |
| MSC: | 15A09 |
| MSC: | 15B48 |
| MSC: | 65F10 |
| idZBL: | Zbl 07547199 |
| idMR: | MR4409310 |
| DOI: | 10.21136/AM.2021.0270-20 |
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| Date available: | 2022-04-14T13:36:52Z |
| Last updated: | 2022-09-06 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/150319 |
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