A generalized iterative scheme with computational results concerning the systems of linear equations

Kamsing Nonlaopon; Farooq Ahmed Shah; Khaleel Ahmed; Ghulam Farid; Kamsing Nonlaopon; Farooq Ahmed Shah; Khaleel Ahmed; Ghulam Farid

doi:10.3934/math.2023328

AIMS Mathematics

2023, Volume 8, Issue 3: 6504-6519. doi: 10.3934/math.2023328

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Research article

A generalized iterative scheme with computational results concerning the systems of linear equations

1.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
2.
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan

Received: 29 August 2022 Revised: 14 December 2022 Accepted: 20 December 2022 Published: 04 January 2023
MSC : 65F10, 90C30

In this article, a new generalized iterative technique is presented for finding the approximate solution of a system of linear equations $ Ax = b $. The efficiency of iterative technique is analyzed by implementing it on some examples, and then comparing with existing methods. A parameter introduced in the method plays very vital role for a better and rapid solution. Convergence analysis is also examined. Findings of this paper may stimulate further research in this area.
- iterative method,
- convergence analysis,
- Gauss-Seidel method,
- sparse matrix,
- AOR method
Citation: Kamsing Nonlaopon, Farooq Ahmed Shah, Khaleel Ahmed, Ghulam Farid. A generalized iterative scheme with computational results concerning the systems of linear equations[J]. AIMS Mathematics, 2023, 8(3): 6504-6519. doi: 10.3934/math.2023328

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Abstract

In this article, a new generalized iterative technique is presented for finding the approximate solution of a system of linear equations $ Ax = b $. The efficiency of iterative technique is analyzed by implementing it on some examples, and then comparing with existing methods. A parameter introduced in the method plays very vital role for a better and rapid solution. Convergence analysis is also examined. Findings of this paper may stimulate further research in this area.

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