Abstract
We propose an approach to enhance the performance of a diagonal variant of secant method for solving large‐scale systems of nonlinear equations. In this approach, we consider diagonal secant method using data from two preceding steps rather than a single step derived using weak secant equation to improve the updated approximate Jacobian in diagonal form. The numerical results verify that the proposed approach is a clear enhancement in numerical performance.
Highlights
Solving systems of nonlinear equations is becoming more essential in the analysis of complex problems in many research areas
We analyze the performance of 2-MFDN method compared to four NewtonLike methods
The numerical results presented in this paper shows that 2-MFDN method is a good alternative to MFDN method especially for extremely large systems
Summary
Solving systems of nonlinear equations is becoming more essential in the analysis of complex problems in many research areas. It is imperative to mention that some efforts have been already carried out in order to eliminate the well-known shortcomings of Newton’s method for solving systems of nonlinear equations, large-scale systems. These so-called revised Newton-type methods include Chord-Newton method, inexact Newton’s method, quasi-Newton’s method, and so forth e.g., see 1–4. Broyden’s method 5 and Chord’s Newton’s method need to store an n × n matrix, and their floating points operations are O n2 To deal with these disadvantages, a diagonally Newton’s method has been suggested by Leong et al 6 by approximating the Jacobian matrix into nonsingular diagonal matrix and updated in every iteration.
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