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Mathematics of Computation

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The convergence of single-rank quasi-Newton methods


Author: C. G. Broyden
Journal: Math. Comp. 24 (1970), 365-382
MSC: Primary 65.50
DOI: https://doi.org/10.1090/S0025-5718-1970-0279993-0
MathSciNet review: 0279993
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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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DOI: https://doi.org/10.1090/S0025-5718-1970-0279993-0
Keywords: Nonlinear algebraic systems, quasi-Newton methods, single-rank methods
Article copyright: © Copyright 1970 American Mathematical Society