Derivative free Newton-type method for fuzzy nonlinear equations

Volume 34, Issue 3, pp 234--242 https://dx.doi.org/10.22436/jmcs.034.03.03

Publication Date: March 18, 2024 Submission Date: December 30, 2023 Revision Date: January 15, 2024 Accteptance Date: February 02, 2024

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Authors

M. A. Aal - Department of Basic Sciences, Faculty of Arts and Educational Sciences, Middle East University, Amman 11831, Jordan.

Abstract

One of the effective techniques for nonlinear equation is the Newton algorithm. In the event that the system's nonsingular Jacobian is found close to the solution, this method's convergence is guaranteed, and its rate is quadratic. Any deviation from this specified condition, such as the presence of a singular Jacobian, would, however, lead to an inadequate convergence or possibly the loss of convergence. This study constructs a derivative quasi-Newton method for large-scale nonlinear equation systems, particularly, when the system contains fuzzy coefficient rather that crisp coefficient. This modification is based on a recent method available in literature. The convergence result of the proposed method has been discussed under suitable assumptions. Preliminary obtained results show that the new algorithm is computationally much faster and promising. An interesting feature of the proposed scheme is that despite the fact that the Jacobian matrix is singular in the neighborhood of the solution, the new algorithm was still able to converge to the solution point.

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Keywords

• Nonlinear equations
• fuzzy
• Jacobian
• inverse Jacobian.

MSC

•  65H11
•  65K05

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