A new quasi-Newton method based on adjoint Broyden updates for symmetric nonlinear equations

摘要

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 $F'(x_{k+1})$ along direction $s_k$ exactly, but also shares some nice properties such as positive definiteness 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.