A Newton's-like method with extra updating strategy for solving singular fuzzy nonlinear equations

Mustafa, Mamat and Mohammed Yusuf, Waziri and Hafiza Aisha, A. (2014) A Newton's-like method with extra updating strategy for solving singular fuzzy nonlinear equations. Applied Mathematical Sciences, 8 (141). pp. 7047-7057. ISSN 1312885X [P]

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Abstract

The basic requirement of Newtons method in solving systems of nonlinear equations is, the Jacobian must be non-singular. Violating this condition, i.e. the Jacobian to be singular the convergence is too slow and may even be lost. This condition restricts to some extent the application of Newton method. In this paper we suggest a new approach for solving fuzzy nonlinear equations where the Jacobian is singular, via incorporating extra updating and restarting strategies in Newton’s method . The anticipation has been to bypass the point(s) in which the Jacobian is singular. Some numerical experiments have been reported, to show the efficiency of our approach and the results are compared with classical Newton’s method.

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