Composite refinement techniques for solving linear systems
Abstract
A composite refinement approach for stationary iterative methods is introduced. Two new formulas (RJGS and RGSJ) are compared with the classical forms. Rates of convergence of the introduced composite formulas (RJGS and RGSJ) are well established. The efficient performance of the new forms is established theoretically and confirmed through numerical examples. The decrease in the required number of iterations for convergence is established through the calculation of the spectral radius of the iteration matrices. The algorithmic structure of the new formulas is announced. Three numerical examples with different convergent properties are considered. The calculations are performed with the help of computer algebra software Mathematica.
Copyright © 2022 Sh. A. Meligy, I. K. Youssef. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
S. A. Meligy, I. K. Youssef, Composite refinement techniques for solving linear systems, J. Math. Comput. Sci. 12 (2022), 145. https://doi.org/10.28919/jmcs/7344
BibTeX
@article{Meligy2022,
author = {Meligy, Sh. A. and Youssef, I. K.},
title = {Composite refinement techniques for solving linear systems},
journal = {J. Math. Comput. Sci.},
volume = {12},
year = {2022},
pages = {145},
doi = {10.28919/jmcs/7344}
}