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International Journal of Mathematics and Mathematical Sciences
Volume 14, Issue 2, Pages 349-361
http://dx.doi.org/10.1155/S016117129100042X

On a general convergence for Broyden like update method

Department of Applied Mathematics, Calcutta University, 92, A.P.C. Road, Calcutta 700009, India

Received 7 December 1987; Revised 20 November 1990

Copyright © 1991 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The role of Broyden's method as a powerful quasi-Newton method for solving unconstrained optimization problems or a system of nonlinear algebraic equations is well known. We offer here a general convergence criterion for a method akin to Broyden's method in Rn. The approach is different from those of other convergence proofs which are available only for the direct prediction methods.