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The robust principal component analysis (RPCA) decomposes a data matrix into a low-rank part and a sparse part. There are mainly two types of algorithms for RPCA. The first type of algorithm applies regularization terms on the singular…
We use the well-known observation that the solutions of Jacobi's differential equation can be represented via non-oscillatory phase and amplitude functions to develop a fast algorithm for computing multi-dimensional Jacobi polynomial…
The cross-product matrix-based CJ-FEAST SVDsolver proposed previously by the authors is shown to compute the left singular vector possibly much less accurately than the right singular vector and may be numerically backward unstable when a…
Matrix completion is a widely used technique for image inpainting and personalized recommender system, etc. In this work, we focus on accelerating the matrix completion using faster randomized singular value decomposition (rSVD). Firstly,…
The generalized singular value decomposition (GSVD, a.k.a. "SVD triplet", "duality diagram" approach) provides a unified strategy and basis to perform nearly all of the most common multivariate analyses (e.g., principal components,…
A new algorithm to compute the restricted singular value decomposition of dense matrices is presented. Like Zha's method \cite{Zha92}, the new algorithm uses an implicit Kogbetliantz iteration, but with four major innovations. The first…
The tensor Singular Value Decomposition (t-SVD) for third order tensors that was proposed by Kilmer and Martin~\cite{2011kilmer} has been applied successfully in many fields, such as computed tomography, facial recognition, and video…
An efficient Singular Value Decomposition (SVD) algorithm is an important tool for distributed and streaming computation in big data problems. It is observed that update of singular vectors of a rank-1 perturbed matrix is similar to a…
In this paper, we present a fast implementation of the Singular Value Thresholding (SVT) algorithm for matrix completion. A rank-revealing randomized singular value decomposition (R3SVD) algorithm is used to adaptively carry out partial…
In this paper, we consider spectral approximation of fractional differential equations (FDEs). A main ingredient of our approach is to define a new class of generalized Jacobi functions (GJFs), which is intrinsically related to fractional…
The singular value decomposition (SVD) of a matrix is a powerful tool for many matrix computation problems. In this paper, we consider generalizing the standard SVD to analyze and compute the regularized solution of linear ill-posed…
The singular value decomposition (SVD) is a crucial tool in machine learning and statistical data analysis. However, it is highly susceptible to outliers in the data matrix. Existing robust SVD algorithms often sacrifice speed for…
The Jacobi-Davidson method is one of the most popular approaches for iteratively computing a few eigenvalues and their associated eigenvectors of a large matrix. The key of this method is to expand the search subspace via solving the…
Singular value decomposition (SVD) is widely used in wireless systems, including multiple-input multiple-output (MIMO) processing and dimension reduction in distributed MIMO (D-MIMO). However, the iterative nature of decomposition methods…
Correspondence analysis, multiple correspondence analysis and their discriminant counterparts (i.e., discriminant simple correspondence analysis and discriminant multiple correspondence analysis) are methods of choice for analyzing…
Singular Value Decomposition (SVD) is the basic body of many statistical algorithms and few users question whether SVD is properly handling its job. SVD aims at evaluating the decomposition that best approximates a data matrix, given some…
An enhanced Kogbetliantz method for the singular value decomposition (SVD) of general matrices of order two is proposed. The method consists of three phases: an almost exact prescaling, that can be beneficial to the LAPACK's xLASV2 routine…
We present a relative forward error analysis of a mixed-precision preconditioned one-sided Jacobi algorithm, analogous to a two-sided version introduced in [N. J. Higham, F. Tisseur, M. Webb and Z. Zhou, SIAM J. Matrix Anal. Appl. 46…
The generalized singular value decomposition (GSVD) of a matrix pair $\{A, L\}$ with $A\in\mathbb{R}^{m\times n}$ and $L\in\mathbb{R}^{p\times n}$ generalizes the singular value decomposition (SVD) of a single matrix. In this paper, we…
Recently, there has been a lot of research into tensor singular value decomposition (t-SVD) by using discrete Fourier transform (DFT) matrix. The main aims of this paper are to propose and study tensor singular value decomposition based on…