On the global convergence of Broyden's method

Authors:
J. J. Moré and J. A. Trangenstein

Journal:
Math. Comp. **30** (1976), 523-540

MSC:
Primary 65H10

DOI:
https://doi.org/10.1090/S0025-5718-1976-0418451-2

MathSciNet review:
0418451

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Abstract: We consider Broyden's 1965 method for solving nonlinear equations. If the mapping is linear, then a simple modification of this method guarantees global and *Q*-superlinear convergence. For nonlinear mappings it is shown that the hybrid strategy for nonlinear equations due to Powell leads to *R*-superlinear convergence provided the search directions form a uniformly linearly independent sequence. We then explore this last concept and its connection with Broyden's method. Finally, we point out how the above results extend to Powell's symmetric version of Broyden's method.

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DOI:
https://doi.org/10.1090/S0025-5718-1976-0418451-2

Article copyright:
© Copyright 1976
American Mathematical Society