Randomized algorithms and theory for rank estimation and least squares

Thesis

This thesis is concerned with randomized algorithms for two matrix problems: numerical rank estimation, with extensions to low-rank approximation, and numerical solutions to least squares (LS) problems. As the dimensions of matrix problems in modern computational settings grow, classical algorithms become increasingly insufficient in terms of computational, communication, and storage costs. Randomized algorithms have been shown to provide excellent alternatives in large-scale settings, and...

Expand abstract

Authors: Meier, M

• DOI: 10.5287/ora-6rjwapeed
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: numerical stability; inverse problems; preconditioning; randomized numerical linear algebra; rank estimation; least squares; iterative solvers; numerical linear algebra; regularization
• Subjects: Mathematics