Some Convergence Properties of Broyden's Method
NBER Working Paper No. 175
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.
Document Object Identifier (DOI): 10.3386/w0175
Published: 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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