TY - JOUR
AU - Gay, David M
TI - Some Convergence Properties of Broyden's Method
JF - National Bureau of Economic Research Working Paper Series
VL - No. 175
PY - 1977
Y2 - July 1977
DO - 10.3386/w0175
UR - http://www.nber.org/papers/w0175
L1 - http://www.nber.org/papers/w0175.pdf
N1 - Author contact info:
David M. Gay
AB - 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.
ER -