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Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices

Author

Listed:
  • Jean-Paul Chehab

    (LAMFA, UMR CNRS 7352, Université de Picardie Jules Verne, 33 rue Saint Leu, 80039 Amiens, France)

  • Marcos Raydan

    (Departamento de Cómputo Científico y Estadística, Universidad Simón Bolívar, Ap. 89000, Caracas 1080-A, Venezuela)

Abstract

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.

Suggested Citation

  • Jean-Paul Chehab & Marcos Raydan, 2016. "Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices," Mathematics, MDPI, vol. 4(3), pages 1-20, July.
    • Handle: RePEc:gam:jmathe:v:4:y:2016:i:3:p:46-:d:73666
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