DMCA
Fast Singular Value Thresholding without Singular Value Decomposition
| Citations: | 12 - 2 self |
BibTeX
@MISC{Cai_fastsingular,
author = {Jian-feng Cai and Stanley Osher},
title = {Fast Singular Value Thresholding without Singular Value Decomposition},
year = {}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
Singularvaluethresholding(SVT)is abasic subroutineinmanypopularnumerical schemes for solving nuclearnormminimization thatarises fromlow-rankmatrixrecoveryproblemssuchasmatrixcompletion. The conventional approach for SVT is first to find the singular value decomposition (SVD) and then to shrink the singular values. However, such an approach is time-consuming under some circumstances, especially when the rank of the resulting matrix is not significantly low compared to its dimension. In this paper, we propose a fast algorithm for directly computing SVT for general dense matrices without usingSVDs. Ouralgorithm isbasedonmatrixNewtoniteration for matrixfunctions, andtheconvergence is theoretically guaranteed. Numerical experiments show that our proposed algorithm is more efficient than the SVD-based approaches for general dense matrices. 1
