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 | References | Similar Articles | Additional Information

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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Additional Information

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