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

Dennis, J. E.

doi:10.1090/S0025-5718-1971-0295560-8

On the convergence of Broyden’s method for nonlinear systems of equations
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Math. Comp. 25 (1971), 559-567 Request permission

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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