The Newton-arithmetic mean method for the solution of systems of nonlinear equations.
type: Item
instance of: scholarly article
title: The Newton-arithmetic mean method for the solution of systems of nonlinear equations.
zbMATH Open document ID: 1047.65031
DOI: 10.1016/S0096-3003(01)00265-X
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: Newton-iterative methods for large systems of nonlinear equations with a block-structured Jacobian are considered. For solving the linear system at each stage of Newton's method the arithmetic mean method is considered, which is based on two particular block-diagonal splitting matrices for the Jacobian, and, therefore, is well suited for implementation on parallel computers. The convergence of the method is analyzed for systems whose Jacobian satisfies an affine invariant Lipschitz condition. The case of weakly nonlinear systems, which arise, for example, from the discretization of semi-linear elliptic systems, is considered in more details, and numerical experiments are reported for such a problem.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 1861282
zbMATH Keywords: Newton-iterative method
zbMATH Keywords: arithmetic mean method
zbMATH Keywords: affine invariance
zbMATH Keywords: weakly nonlinear systems
zbMATH Keywords: parallel computation
zbMATH Keywords: large systems of nonlinear equations
zbMATH Keywords: convergence
zbMATH Keywords: semi-linear elliptic system
zbMATH Keywords: numerical experiments
author: Emanuele Galligani
reviewed by: Walter Zulehner
describes a project that uses: KELLEY
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1861282