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2016

On the steepest descent algorithm for quadratic functions

4 years 9 months ago
On the steepest descent algorithm for quadratic functions
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.
Clóvis C. Gonzaga, Ruana M. Schneider
Added 31 Mar 2016
Updated 31 Mar 2016
Type Journal
Year 2016
Where COAP
Authors Clóvis C. Gonzaga, Ruana M. Schneider
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