Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices
LAMFA, UMR CNRS 7352, Université de Picardie Jules Verne, 33 rue Saint Leu, 80039 Amiens, France
Departamento de Cómputo Científico y Estadística, Universidad Simón Bolívar, Ap. 89000, Caracas 1080-A, Venezuela
Author to whom correspondence should be addressed.
Academic Editor: Khalide Jbilou
Received: 11 May 2016 / Revised: 29 June 2016 / Accepted: 1 July 2016 / Published: 9 July 2016
We focus on inverse preconditioners based on minimizing
is the preconditioned matrix and A
is symmetric and positive definite. We present and analyze gradient-type methods to minimize
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
on the feasible set. Preliminary and encouraging numerical results are also presented in which dense and sparse approximations are included.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
Chehab, J.-P.; Raydan, M. Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices. Mathematics 2016, 4, 46.
Chehab J-P, Raydan M. Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices. Mathematics. 2016; 4(3):46.
Chehab, Jean-Paul; Raydan, Marcos. 2016. "Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices." Mathematics 4, no. 3: 46.
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