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R. Byrd, J. Nocedal, and Y. Yuan, “Global convergence of a class of quasi-Newton methods on convex problems,” SIAM Journal on Numerical Analysis, No. 24, pp. 1171–1189, 1987.

has been cited by the following article:

• TITLE: A Rank-One Fitting Method with Descent Direction for Solving Symmetric Nonlinear Equations

  AUTHORS: Gonglin YUAN, Zhongxing WANG, Zengxin WEI

  KEYWORDS: Rank-One Update, Global Convergence, Nonlinear Equations, Descent Direction

  JOURNAL NAME: International Journal of Communications, Network and System Sciences, Vol.2 No.6, September 22, 2009

  ABSTRACT: In this paper, a rank-one updated method for solving symmetric nonlinear equations is proposed. This method possesses some features: 1) The updated matrix is positive definite whatever line search technique is used; 2) The search direction is descent for the norm function; 3) The global convergence of the given method is established under reasonable conditions. Numerical results show that the presented method is interesting.