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Title: High performance Cholesky and symmetric indefinite factorizations with applications
Author: Hogg, Jonathan David
ISNI:       0000 0004 2727 954X
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2010
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The process of factorizing a symmetric matrix using the Cholesky (LLT ) or indefinite (LDLT ) factorization of A allows the efficient solution of systems Ax = b when A is symmetric. This thesis describes the development of new serial and parallel techniques for this problem and demonstrates them in the setting of interior point methods. In serial, the effects of various scalings are reported, and a fast and robust mixed precision sparse solver is developed. In parallel, DAG-driven dense and sparse factorizations are developed for the positive definite case. These achieve performance comparable with other world-leading implementations using a novel algorithm in the same family as those given by Buttari et al. for the dense problem. Performance of these techniques in the context of an interior point method is assessed.
Supervisor: Hall, Julian. ; Grothey, Andreas. ; Gondzio, Jacek. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: symmetric matrix ; Cholesky factorization ; sparse symmetric linear systems ; DAG-based