On the global convergence of Broyden's method
Authors:
J. J. Moré and J. A. Trangenstein
Journal:
Math. Comp. 30 (1976), 523540
MSC:
Primary 65H10
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 Qsuperlinear convergence. For nonlinear mappings it is shown that the hybrid strategy for nonlinear equations due to Powell leads to Rsuperlinear 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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 S. M. THOMAS, Sequential Estimation Techniques for QuasiNewton Algorithms, Cornell University Ph.D. Thesis, 1974.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197604184512
PII:
S 00255718(1976)04184512
Article copyright:
© Copyright 1976 American Mathematical Society
