Open Access
2014 Global Convergence of Schubert’s Method for Solving Sparse Nonlinear Equations
Huiping Cao
Abstr. Appl. Anal. 2014: 1-12 (2014). DOI: 10.1155/2014/251587


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.


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Huiping Cao. "Global Convergence of Schubert’s Method for Solving Sparse Nonlinear Equations." Abstr. Appl. Anal. 2014 1 - 12, 2014.


Published: 2014
First available in Project Euclid: 27 February 2015

zbMATH: 07022005
MathSciNet: MR3272188
Digital Object Identifier: 10.1155/2014/251587

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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