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Optimally conditioned scaled ABS algorithms for linear systems
Authors:E. Spedicato  Z. Yang
Affiliation:(1) Department of Mathematics, University of Bergamo, Bergamo, Italy;(2) Department of Applied Mathematics, Dalian University of Technology, Dalian, China
Abstract:
Using a strict bound of Spedicato to the condition number of bordered positive-definite matrices, we show that the scaling parameter in the ABS class for linear systems can always be chosen so that the bound of a certain update matrix is globally minimized. Moreover, if the scaling parameter is so chosen at every iteration, then the condition number itself is globally minimized. The resulting class of optimally conditioned algorithms contains as a special case the class of optimally stable algorithms in the sense of Broyden.This work was done in the framework of research supported by MPI, Rome, Italy, 60% Program.
Keywords:ABS algorithms  bordered positive-definite matrices  condition numbers  linear systems  optimal conditioning  optimal stability
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