New search direction of steepest descent method for solving large linear systems

الملخص EN

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.