Randomized Algorithms for Solving Singular Value Decomposition Problems with Matlab Toolbox

Abstract

This thesis gives an overview of the state-of-the-art randomized linear algebra algorithms for singular value decomposition (SVD), including the presentation of existing pseudo-codes and theoretical error analysis. Our main focus is on presenting numerical experiments illustrating image restoration using various randomized singular value decomposition (RSVD) methods; theoretical error bounds, computed errors, and canonical angles analysis for these RSVD algorithms. This thesis also comes with a newly developed Matlab toolbox that contains implementations and test examples for some of the state-of-the-art randomized numerical linear algebra algorithms.