Global Convergence of Schubert's Method for Solving Sparse Nonlinear Equations. (14th October 2014)

• Record Type: Journal Article
• Authors: Cao, Huiping
• Other Names: Peng Shuangjie Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-10-14
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/251587
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : 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.