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Partially Updated Switching-Method for systems of nonlinear equations

โœ Scribed by S. Bellavia; M.G. Gasparo; M. Macconi

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
619 KB
Volume
76
Category
Article
ISSN
0377-0427

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โœฆ Synopsis

A hybrid~method for solving systems of n nonlinear equations is given. The method does not use derivative information and is especially attractive when good starting points are not available and the given system is expensive to evaluate. It is shown that, after a few steps, each iteration requires (2k + 1) function evaluations where k, 1 ~< k ~< n, is chosen so as to have an efficient algorithm. Global convergence results are given and superlinear convergence is established. Some numerical results show the numerical performance of the proposed method.

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A Switching-Method for nonlinear systems
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In this paper, a partially asynchronous block Broyden method is presented for solving nonlinear systems of equations of the form F(x)= 0. Sufficient conditions that guarantee its local convergence are given. In particular, local convergence is shown when the Jacobian F'(x\*) is an H-matrix, where x\