5 papers
Precision-induced Adaptive Randomized Low-Rank Approximation for SVD and Matrix Inversion
Weiwei Xu, Weijie Shen, Zhengjian Bai +1
Singular value decomposition (SVD) and matrix inversion are ubiquitous in scientific computing. Both tasks are computationally demanding for large scale matrices. Existing algorith…
A Novel Adaptive Low-Rank Matrix Approximation Method for Image Compression and Reconstruction
Weiwei Xu, Weijie Shen, Chang Liu +1
Low-rank matrix approximation plays an important role in various applications such as image processing, signal processing and data analysis. The existing methods require a guess of…
Two-sided uniformly randomized GSVD for large-scale discrete ill-posed problems with Tikhonov regularizations
Weiwei Xu, Weijie Shen, Zheng-Jian Bai
The generalized singular value decomposition (GSVD) is a powerful tool for solving discrete ill-posed problems. In this paper, we propose a two-sided uniformly randomized GSVD algo…
Efficient Orthogonal Decomposition with Automatic Basis Extraction for Low-Rank Matrix Approximation
Weijie Shen, Weiwei Xu, Lei Zhu
Low-rank matrix approximation play a ubiquitous role in various applications such as image processing, signal processing, and data analysis. Recently, random algorithms of low-rank…
Fast randomized algorithms for low-rank matrix approximations with applications in global comparative analysis of a class of data sets
Weiwei Xu, Weijie Shen, Wen Li +2
Generalized singular values (GSVs) play an essential role in the comparative analysis. In the real world data for comparative analysis, both data matrices are usually numerically l…