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Some Convergence Properties of Broyden's Method

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  • David M. Gay

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.

Suggested Citation

  • David M. Gay, 1977. "Some Convergence Properties of Broyden's Method," NBER Working Papers 0175, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:0175
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    1. David M. Gay & Robert B. Schnabel, 1977. "Solving Systems of Non-Linear Equations by Broyden's Method with Projected Updates," NBER Working Papers 0169, National Bureau of Economic Research, Inc.
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