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@techreport{NBERw0175,
title = "Some Convergence Properties of Broyden's Method",
author = "Gay, David M",
institution = "National Bureau of Economic Research",
type = "Working Paper",
series = "Working Paper Series",
number = "175",
year = "1977",
month = "July",
doi = {10.3386/w0175},
URL = "http://www.nber.org/papers/w0175",
abstract = {In 1965 Broyden introduced a family of algorithms called(rank-one) quasi-New-ton methods for iteratively solving systems of nonlinear equations. We show that when any member of this family is applied to an n x n nonsingular system of linear equations and direct-prediction steps are taken every second iteration, then the solution is found in at most 2n steps. Specializing to the particular family member known as Broydenâ€™s (good) method, we use this result to show that Broyden's method enjoys local 2n-step Q-quadratic convergence on nonlinear problems.},
}