Some Convergence Properties of Broyden's Method

David M. Gay

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

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Year of publication:	July 1977
Authors:	Gay, David M.
Institutions:	National Bureau of Economic Research (contributor)
Publisher:	Cambridge, Mass : National Bureau of Economic Research
Subject:	Theorie \| Theory \| Wirtschaftliche Konvergenz \| Economic convergence

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