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On the steepest descent algorithm for quadratic functions

Clovis Gonzaga (ccgonzaga1***at***gmail.com)
Ruana Schneider (ruanamaira***at***gmail.com)

Abstract: The steepest descent algorithm with exact line searches (Cauchy algorithm) is inefficient, generating oscillating step lengths and a sequence of points converging to the span of the eigenvectors associated with the extreme eigenvalues. The performance becomes very good if a short step is taken at every (say) 10 iterations. We show a new method for estimating short steps, and propose a method alternating Cauchy and short steps. Finally, we use the roots of a certain Chebyshev polynomial to further accelerate the method.

Keywords: Steepest descent algorithms, Quadratic functions

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: Federal Univ. of Santa Catarina, Brazil, May/2015

Download: [PDF]

Entry Submitted: 06/15/2015
Entry Accepted: 06/15/2015
Entry Last Modified: 07/09/2015

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