The Chaotic Nature of Faster Gradient Descent Methods |
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| Authors: | Kees van den Doel Uri Ascher |
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| Affiliation: | (1) Environmental Research Institute of Michigan, 1501 Wilson Boulevard, 22209 Arlington, VA, USA;(2) Computer Science Department, University of Missouri, 65401 Rolla, MO, USA;(3) Neural Systems Section, National Institute of Neurological and Communicative Disorders and Stroke, NIH, 9000 Rockville Pike, 20892 Bethesda, MD, USA; |
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| Abstract: | The steepest descent method for large linear systems is well-known to often converge very slowly, with the number of iterations
required being about the same as that obtained by utilizing a gradient descent method with the best constant step size and
growing proportionally to the condition number. Faster gradient descent methods must occasionally resort to significantly
larger step sizes, which in turn yields a rather non-monotone decrease pattern in the residual vector norm. |
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