Some Convergence Properties of Broyden's Method

David M. Gay

No 175, NBER Working Papers from National Bureau of Economic Research, Inc

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 Broyden's (good) method, we use this result to show that Broyden's method enjoys local 2n-step Q-quadratic convergence on nonlinear problems.

Date: 1977-07
Note: TWP
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Published as Gay, David M. "Some Convergence Properties of Broyden's Method." SIAM Journal on Numerical Analysis 16, 4 (Aug 1979): 623-630.

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