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Title: High performance Cholesky and symmetric indefinite factorizations with applications
Authors: Hogg, Jonathan David
Supervisor(s): Hall, Julian
Grothey, Andreas
Gondzio, Jacek
Issue Date: 2010
Publisher: The University of Edinburgh
Abstract: 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.
Keywords: symmetric matrix
Cholesky factorization
sparse symmetric linear systems
Appears in Collections:Mathematics thesis and dissertation collection

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