Modified Cholesky Decomposition and Applications

McSweeney, Thomas (2017) Modified Cholesky Decomposition and Applications. Masters thesis, University of Manchester.

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Abstract

The modified Cholesky decomposition is one of the standard tools in various areas of mathematics for dealing with symmetric indefinite matrices that are required to be positive definite. We survey the literature and determine which of the existing modified Cholesky algorithms is most suitable for inclusion in the Numerical Algorithms Group (NAG) software library, focussing in particular on the algorithms of Gill, Murray and Wright, Schnabel and Eskow, Cheng and Higham, and Moré and Sorensen. In order to make this determination we consider how best to take advantage of modern computer architectures and existing numerical software. We create an efficient implementation of the chosen algorithm and perform extensive numerical testing to ensure that it works as intended. We then discuss various applications of the modified Cholesky decomposition and show how the new implementation can be used for some of these. In particular, significant attention is devoted to describing how the modified Cholesky decomposition can be used to compute an upper bound on the distance to the nearest correlation matrix.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	modified Cholesky decomposition, nearest correlation matrix, indefinite matrix
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Divisions:	Manchester Institute for the Mathematical Sciences
Depositing User:	Mr Thomas McSweeney
Date Deposited:	14 Nov 2017 08:46
Last Modified:	14 Nov 2017 08:46
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2599

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