A new filled function method for an unconstrained nonlinear equation

Authors:
Chengjun Wang;Ronghua Luo;Kun Wu;Boshun Han
Affiliations:
Department of Finance and Trade, Canvard College, Beijing Technology and Business University, Beijing 101118, PR China;Department of Finance and Trade, Canvard College, Beijing Technology and Business University, Beijing 101118, PR China;Department of Finance and Trade, Canvard College, Beijing Technology and Business University, Beijing 101118, PR China;Department of Mathematics, Shanghai University, Shanghai 200444, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

In this paper, we transform an unconstrained system of nonlinear equations into a special optimization problem. A new filled function is constructed by employing the special properties of the transformed optimization problem. Theoretical and numerical properties of the proposed filled function are investigated and a solution of the algorithm is proposed. Under some conditions, we can find a solution or an approximate solution to the system of nonlinear equations in finite iterations. The implementation of the algorithm on six test problems is reported with satisfactory numerical results.