A modified Brown algorithm for solving singular nonlinear systems with rank defects

Authors:
Ren-Dong Ge;Zun-Quan Xia;Jian-guo Liu
Affiliations:
Department of Applied Mathematics, Dalian University of Technology, China and Department of Applied Mathematics and Physics, Dalin Nationalities University, China;Department of Applied Mathematics, Dalian University of Technology, China;Department of Applied Mathematics, Dalian University of Technology, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

A modified Brown algorithm for solving a class of singular nonlinear systems, F(x) = 0, where x, F ∈ Rn, is presented. This method is constructed by combining the discreted Brown algorithm with the space transforming method. The second-order information of F(x) at a point is not required calculating, which is different from the tensor method and the Hoy's method. The Q-quadratic convergence of this algorithm and some numerical examples are given as well.