Inverse q-columns updating methods for solving nonlinear systems of equations

Authors:
Luziane Ferreira de Mendonça;Rosana Pérez;Véra Lucia Rocha Lopes
Affiliations:
DMA-IMECC-UNICAMP, 13083-970 Campinas, SP, Brazil;Departamento de Matemáticas, Universidad del Cauca, Popayán (Cauca), Columbia;DMA-IMECC-UNICAMP, 13083-970 Campinas, SP, Brazil
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

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Abstract

In this work new quasi-Newton methods for solving large-scale nonlinear systems of equations are presented. In these methods q ( 1) columns of the approximation of the inverse Jacobian matrix are updated in such a way that the q last secant equations are satisfied (whenever possible) at every iteration. An optimal maximum value for q that makes the method competitive is strongly suggested. The best implementation from the point of view of linear algebra and numerical stability is proposed and a local convergence result for the case q = 2 is proved. Several numerical comparative tests with other quasi-Newton methods are carried out.