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On the convergence of Broyden's method for nonlinear systems of equations


Author: J. E. Dennis
Journal: Math. Comp. 25 (1971), 559-567
MSC: Primary 65H10
DOI: https://doi.org/10.1090/S0025-5718-1971-0295560-8
MathSciNet review: 0295560
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Abstract: This paper uses majorant techniques to study the convergence of Broyden's single-rank update method for nonlinear systems of equations. It also contains a very elementary proof of the local convergence of the method. The heart of the method is a procedure for generating an approximation to the Jacobian of the system using only information on hand and not requiring partial derivatives.


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DOI: https://doi.org/10.1090/S0025-5718-1971-0295560-8
Keywords: Nonlinear vector equations, Newton-like methods, Davidon methods, iteration, nonlinear majorization
Article copyright: © Copyright 1971 American Mathematical Society