General Letters in Mathematics

Volume 12 - Issue 2 (2) | PP: 57 - 63 Language : English
DOI : https://doi.org/10.31559/glm2022.12.2.2
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New search direction of steepest descent method for solving large linear systems

Ayad Ramadhan Ali ,
Bayda Ghanim Fathi
Received Date Revised Date Accepted Date Publication Date
16/4/2022 20/5/2022 28/5/2022 13/8/2022
Abstract
The steepest descent (SD) method is well-known as the simplest method in optimization. In this paper, we propose a new SD search direction for solving system of linear equations Ax = b. We also prove that the proposed SD method with exact line search satisfies descent condition and possesses global convergence properties. This proposed method is motivated by previous work on the SD method by Zubai’ah-Mustafa-Rivaie-Ismail (ZMRI)[2]. Numerical comparisons with a classical SD algorithm and ZMRI algorithm show that this algorithm is very effective depending on the number of iterations (NOI) and CPU time.


How To Cite This Article
Ali , A. R. & Fathi , B. G. (2022). New search direction of steepest descent method for solving large linear systems . General Letters in Mathematics, 12 (2), 57-63, 10.31559/glm2022.12.2.2

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