Global Convergence of Schubert’s Method for Solving Sparse Nonlinear Equations

Global Convergence of Schubert’s Method for Solving Sparse Nonlinear Equations

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 an...

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Main Author: Huiping Cao
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/251587
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spelling doaj-0211e9a89407496ba47f222b14b64cea2020-11-24T20:51:33ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/251587251587Global Convergence of Schubert’s Method for Solving Sparse Nonlinear EquationsHuiping Cao0College of Mathematics and Econometrics, Hunan University, Changsha 410082, ChinaSchubert’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.http://dx.doi.org/10.1155/2014/251587
collection DOAJ
language English
format Article
sources DOAJ
author Huiping Cao
spellingShingle Huiping Cao
Global Convergence of Schubert’s Method for Solving Sparse Nonlinear Equations
Abstract and Applied Analysis
author_facet Huiping Cao
author_sort Huiping Cao
title Global Convergence of Schubert’s Method for Solving Sparse Nonlinear Equations
title_short Global Convergence of Schubert’s Method for Solving Sparse Nonlinear Equations
title_full Global Convergence of Schubert’s Method for Solving Sparse Nonlinear Equations
title_fullStr Global Convergence of Schubert’s Method for Solving Sparse Nonlinear Equations
title_full_unstemmed Global Convergence of Schubert’s Method for Solving Sparse Nonlinear Equations
title_sort global convergence of schubert’s method for solving sparse nonlinear equations
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description 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.
url http://dx.doi.org/10.1155/2014/251587
work_keys_str_mv AT huipingcao globalconvergenceofschubertsmethodforsolvingsparsenonlinearequations
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