The convergence of single-rank quasi-Newton methods

Broyden, C. G.

doi:10.1090/S0025-5718-1970-0279993-0

The convergence of single-rank quasi-Newton methods
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by C. G. Broyden PDF

Math. Comp. 24 (1970), 365-382 Request permission

Abstract:

Analyses of the convergence properties of general quasi-Newton methods are presented, particular attention being paid to how the approximate solutions and the iteration matrices approach their final values. It is further shown that when Broyden’s algorithm is applied to linear systems, the error norms are majorised by a superlinearly convergent sequence of an unusual kind.

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