Abstract
This paper presents Quasi Newton’s (QN) approach for solving fuzzy nonlinear equations. The method considers an approximation of the Jacobian matrix which is updated as the iteration progresses. Numerical illustrations are carried, and the results shows that the proposed method is very encouraging.
Highlights
Systems of nonlinear equations of the form F(x) = 0 (1)where F: Rn → Rn is a real-valued function of a vector, is widely used in areas such as engineering, mathematics, computer science and social science
We present the algorithm for our proposed approach (Newton-Broyden’s Method) as follows: Algorithm 1: Newton-Broyden’s Method (NBM)
Two examples where considered to illustrate the performance of the proposed method for solving fuzzy nonlinear equation
Summary
Where F: Rn → Rn is a real-valued function of a vector, is widely used in areas such as engineering, mathematics, computer science and social science. Kelley (1995) used Shamanskii-like method to solve nonlinear equations at singular point and Sulaiman et al (2018); Sulaiman et al (2018) further apply the Shamanskii’s approach for fuzzy nonlinear problems These methods do not evaluate the Jacobian at each iteration. We consider a Broyden’s-like method for solving systems of fuzzy nonlinear equations. This method can best be described as belonging to the family of Quasi-Newton’s method.
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