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Axioms 2018, 7(3), 44; https://doi.org/10.3390/axioms7030044

On Partial Cholesky Factorization and a Variant of Quasi-Newton Preconditioners for Symmetric Positive Definite Matrices

Dipartimento di Ingegneria Industriale, Università degli Studi di Firenze, 50134 Florence, Italy
Member of the INdAM Research Group GNCS.
Received: 23 April 2018 / Revised: 19 June 2018 / Accepted: 20 June 2018 / Published: 1 July 2018
(This article belongs to the Special Issue Advanced Numerical Methods in Applied Sciences)
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Abstract

This work studies limited memory preconditioners for linear symmetric positive definite systems of equations. Connections are established between a partial Cholesky factorization from the literature and a variant of Quasi-Newton type preconditioners. Then, a strategy for enhancing the Quasi-Newton preconditioner via available information is proposed. Numerical experiments show the behaviour of the resulting preconditioner. View Full-Text
Keywords: linear systems; preconditioners; Cholesky factorization; limited memory linear systems; preconditioners; Cholesky factorization; limited memory
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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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Morini, B. On Partial Cholesky Factorization and a Variant of Quasi-Newton Preconditioners for Symmetric Positive Definite Matrices. Axioms 2018, 7, 44.

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