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http://dx.doi.org/10.4134/JKMS.j150542

A NEW QUASI-NEWTON METHOD BASED ON ADJOINT BROYDEN UPDATES FOR SYMMETRIC NONLINEAR EQUATIONS  

Cao, Huiping (College of Mathematics and Econometrics Hunan University)
Publication Information
Journal of the Korean Mathematical Society / v.53, no.6, 2016 , pp. 1371-1389 More about this Journal
Abstract
In this paper, we propose a new rank two quasi-Newton method based on adjoint Broyden updates for solving symmetric nonlinear equations, which can be seen as a class of adjoint BFGS method. The new rank two quasi-Newton update not only can guarantee that $B_{k+1}$ approximates Jacobian $F^{\prime}(x_{k+1})$ along direction $s_k$ exactly, but also shares some nice properties such as positive deniteness and least change property with BFGS method. Under suitable conditions, the proposed method converges globally and superlinearly. Some preliminary numerical results are reported to show that the proposed method is effective and competitive.
Keywords
adjoint Broyden update; quasi-Newton method; symmetric nonlinear equations; global convergence; superlinear convergence;
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