Some Convergence Properties of Broyden's Method / David M. Gay.

By:

Gay, David M

Contributor(s):

National Bureau of Economic Research

Material type: Text

TextSeries: Working Paper Series (National Bureau of Economic Research) ; no. w0175.Publication details: Cambridge, Mass. National Bureau of Economic Research 1977.Description: 1 online resource: illustrations (black and white)Online resources:

Available additional physical forms:

Hardcopy version available to institutional subscribers

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.

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Item type	Home library	Collection	Call number	Status	Date due	Barcode	Item holds
Working Paper	Biblioteca Digital	Colección NBER	nber w0175 (Browse shelf(Opens below))	Not For Loan

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July 1977.

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.