Energy-based sampling strategies for the low-rank approximation of positive semidefinite matrices

Hutchings, Matthew 2024. Energy-based sampling strategies for the low-rank approximation of positive semidefinite matrices. PhD Thesis, Cardiff University. Item availability restricted.

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Abstract

This thesis focuses on the design of efficient strategies for the low-rank approximation of positive semidefinite matrices via column sampling. A special emphasis is placed on investigating the properties of the energy setting, which relates the lowrank approximation of Hilbert-Schmidt integral operators with the approximation of potentials in reproducing kernel Hilbert spaces. The implications of the energy setting in the matrix framework are investigated, leading to the definition of differentiable surrogate error maps for the characterisation of low-rank approximations. Classes of gradient-based sampling strategies leveraging the properties of these error maps are then proposed and analysed, and the possibility to improve the numerical efficiency of these approaches via stochastic approximations is explored.

Item Type:	Thesis (PhD)
Date Type:	Completion
Status:	Unpublished
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Funders:	EPSRC
Date of First Compliant Deposit:	30 October 2024
Last Modified:	30 Oct 2024 09:55
URI:	https://orca.cardiff.ac.uk/id/eprint/173514

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