Why Broyden's Nonsymmetric Method Terminates on linear equations
Why Broyden's Nonsymmetric Method Terminates on linear equations
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Date
1998-10-15
Authors
O'Leary, Dianne P.
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Abstract
Abstract. The family of algorithms introduced by Broyden in 1965 for
solving systems of nonlinear equations has been used quite effectively on
a variety of problems. In 1979, Gay proved the then surprising result
that the algorithms terminate in at most 2n steps on linear problems with
n variables. His very clever proof gives no insight into properties of
the intermediate iterates, however. In this work we show that Broyden's
methods are projection methods, forcing the residuals to lie in a nested
set of subspaces of decreasing dimension.
(Also cross-referenced as UMIACS-TR-93-23)