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

Format:

Book

Author/Creator:

Gay, David M.

Contributor:

National Bureau of Economic Research.

Series:

Working Paper Series (National Bureau of Economic Research) no. w0175.

NBER working paper series no. w0175

Language:

English

Subjects (All):

Iterative methods (Mathematics).

Evolution equations--Numerical solutions.

Evolution equations.

Physical Description:

1 online resource: illustrations (black and white);

Place of Publication:

Cambridge, Mass. National Bureau of Economic Research 1977.

Cambridge, Mass. : National Bureau of Economic Research, 1977.

Summary:

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.

Notes:

Print version record

July 1977.