Global convergence of Schubert's method for solving sparse nonlinear equations
type: Item
instance of: scholarly article
title: Global convergence of Schubert's method for solving sparse nonlinear equations
zbMATH Open document ID: 1470.65101
DOI: 10.1155/2014/251587
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Schubert's method is an extension of Broyden's method for solving sparse nonlinear equations, which can preserve the zero-nonzero structure defined by the sparse Jacobian matrix and can retain many good properties of Broyden's method. In particular, Schubert's method has been proved to be locally and \(q\)-superlinearly convergent. In this paper, we globalize Schubert's method by using a nonmonotone line search. Under appropriate conditions, we show that the proposed algorithm converges globally and superlinearly. Some preliminary numerical experiments are presented, which demonstrate that our algorithm is effective for large-scale problems.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 39A60
zbMATH DE Number: 7022005
author: Huiping Cao
describes a project that uses: minpack
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/251587
OpenAlex ID: W2023262135
Wikidata QID: Q59036933
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description: scientific article; zbMATH DE number 7022005