Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices

Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices

We focus on inverse preconditioners based on minimizing F ( X ) = 1 − cos ( X A , I ) , where X A is the preconditioned matrix and A is symmetric and positive definite. We present and analyze gradient-type methods to minimize F ( X ) on a suitable compact set. For this, we use...

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Bibliographic Details
Main Authors: Jean-Paul Chehab, Marcos Raydan
Format: Article
Language:English
Published: MDPI AG 2016-07-01
Series:Mathematics
Subjects:
preconditioning
cones of matrices
gradient method
minimal residual method
Online Access:http://www.mdpi.com/2227-7390/4/3/46
Description
Summary:We focus on inverse preconditioners based on minimizing F ( X ) = 1 − cos ( X A , I ) , where X A is the preconditioned matrix and A is symmetric and positive definite. We present and analyze gradient-type methods to minimize F ( X ) on a suitable compact set. For this, we use the geometrical properties of the non-polyhedral cone of symmetric and positive definite matrices, and also the special properties of F ( X ) on the feasible set. Preliminary and encouraging numerical results are also presented in which dense and sparse approximations are included.
ISSN:2227-7390

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