Matrix Decompositon

Randomized Singular Value Decomposition: A Study

In this project we study randomized Singular Value Decomposition (SVD). Apart from the standard randomized SVD algorithm, two modified versions, one for eliminating the influence of the round-off error and one for adaptively determining a desired error threshold, are introduced and discussed. Their ef- ficiency and stability are demonstrated by experiments on two test matrices, one is a given matrix which has full rank and slowly-decaying singular values and the other one is generated from the numerical solutions of a piece-wise con- stant diffusion equation. A special treatment when the input matrix is positive semi-definite is also discussed and validated with numerical results.