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Article Dans Une Revue Mathematics Année : 2016

Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices

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Résumé

We focus on inverse preconditioners based on minimizing F (X) = 1 - cos (XA, I), where XA 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.

Dates et versions

hal-03621852 , version 1 (28-03-2022)

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Jean-Paul Chehab, Marcos Raydan. Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices. Mathematics , 2016, 4 (3), ⟨10.3390/math4030046⟩. ⟨hal-03621852⟩
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