A Newton Algorithm for the Nearest Correlation Matrix

Borsdorf, Rudiger (2007) A Newton Algorithm for the Nearest Correlation Matrix. Masters thesis, University of Manchester.

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Abstract

Firstly, we describe and investigate the algorithm of Qi and Sun which solves the problem of finding the nearest correlation matrix to a symmetric matrix. This algorithm claims a quadratic convergence. We discuss improving this algorithm's efficiency and reliability and detect a problem when we are aiming at a nearest correlation matrix with a high accuracy, using small error tolerences. As a consequence, we suggest a modified version, based on the algorithm of Qi and Sun, which is also a quadratically convergent algorithm, has improved efficiency and is modified so that the algorithm can return the nearest correlation matrix to high accuracy showing a robust and reliable behaviour. Secondly, we investigate the general alternating projections method and also Higham's alternating projections method for the nearest correlation matrix. We discuss variations of the latter and include a further projection which allows more constraints to be added to the problem. We introduce a new algorithm and compare its convergence behaviour with Higham's alternating projections method.

Item Type: Thesis (Masters)
Uncontrolled Keywords: correlation matrix, positive semidefinite matrix, Newton's method, preconditioning, rounding error, Armijo line search conditions, alternating projections method
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
Depositing User: Nick Higham
Date Deposited: 21 Apr 2008
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1085

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