On the steepest descent algorithm for quadratic functions

Clóvis Gonzaga () and Ruana Schneider ()

Computational Optimization and Applications, 2016, vol. 63, issue 2, 523-542

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) ten 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 methods. Copyright Springer Science+Business Media New York 2016

Date: 2016
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DOI: 10.1007/s10589-015-9775-z

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