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An efficient, accurate and reliable approximation of a matrix by one of lower rank is a fundamental task in numerical linear algebra and signal processing applications. In this paper, we introduce a new matrix decomposition approach termed…

Numerical Analysis · Computer Science 2018-08-15 Maboud F. Kaloorazi , Rodrigo C. de Lamare

The randomized singular value decomposition proposed in [27] has certainly become one of the most well-established randomization-based algorithms in numerical linear algebra. The key ingredient of the entire procedure is the computation of…

Numerical Analysis · Mathematics 2025-08-01 Davide Palitta , Sascha Portaro

Singular value decomposition (SVD) is a standard matrix factorization technique that produces optimal low-rank approximations of matrices. It has diverse applications, including machine learning, data science and signal processing. However,…

Mathematical Software · Computer Science 2019-07-16 Vadim Demchik , Miroslav Bačák , Stefan Bordag

Truncated Singular Value Decomposition (SVD) calculates the closest rank-$k$ approximation of a given input matrix. Selecting the appropriate rank $k$ defines a critical model order choice in most applications of SVD. To obtain a principled…

Information Theory · Computer Science 2013-01-08 Mario Frank , Joachim M. Buhmann

In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value…

Numerical Analysis · Mathematics 2019-09-05 Kazufumi Ito , Bangti Jin

Singular Value Decomposition (SVD) is a powerful tool for multivariate analysis. However, independent computation of the SVD for each sample taken from a bandlimited matrix random process will result in singular value sample paths whose…

Statistics Theory · Mathematics 2007-06-13 D. W. Browne , M. W. Browne , M. P. Fitz

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…

Machine Learning · Statistics 2024-02-16 Sangil Han , Kyoowon Kim , Sungkyu Jung

Learning a dynamical system from input/output data is a fundamental task in the control design pipeline. In the partially observed setting there are two components to identification: parameter estimation to learn the Markov parameters, and…

Optimization and Control · Mathematics 2021-09-08 Han Wang , James Anderson

This paper presents a randomized quaternion singular value decomposition (QSVD) algorithm for low-rank matrix approximation problems, which are widely used in color face recognition, video compression, and signal processing problems. With…

Numerical Analysis · Mathematics 2021-12-28 Qiaohua Liu , Sitao Ling , Zhigang Jia

RSVDPACK is a library of functions for computing low rank approximations of matrices. The library includes functions for computing standard (partial) factorizations such as the Singular Value Decomposition (SVD), and also so called…

Numerical Analysis · Mathematics 2016-08-30 Sergey Voronin , Per-Gunnar Martinsson

Singular Value Decomposition (SVD) is a technique based on linear projection theory, which has been frequently used for data analysis. It constitutes an optimal (in the sense of least squares) decomposition of a matrix in the most relevant…

Data Analysis, Statistics and Probability · Physics 2015-03-17 Pau Erola , Javier Borge-Holthoefer , Sergio Gomez , Alex Arenas

This article studies the problem of decentralized Singular Value Decomposition (d-SVD), which is fundamental in various signal processing applications. Two scenarios are considered depending on the availability of the data matrix under…

Signal Processing · Electrical Eng. & Systems 2025-01-10 Yufan Fan , Marius Pesavento

The randomized singular value decomposition (SVD) has become a popular approach to computing cheap, yet accurate, low-rank approximations to matrices due to its efficiency and strong theoretical guarantees. Recent work by Boull\'e and…

Numerical Analysis · Mathematics 2024-12-10 David Persson , Nicolas Boullé , Daniel Kressner

The randomized singular value decomposition (RSVD) is by now a well established technique for efficiently computing an approximate singular value decomposition of a matrix. Building on the ideas that underpin the RSVD, the recently proposed…

Mathematical Software · Computer Science 2021-04-14 N. Heavner , F. D. Igual , G. Quintana-Ortí , P. G. Martinsson

We propose a new algorithm for the computation of a singular value decomposition (SVD) low-rank approximation of a matrix in the Matrix Product Operator (MPO) format, also called the Tensor Train Matrix format. Our tensor network randomized…

Numerical Analysis · Mathematics 2017-07-26 Kim Batselier , Wenjian Yu , Luca Daniel , Ngai Wong

Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…

Computation · Statistics 2019-11-28 N. Benjamin Erichson , Sergey Voronin , Steven L. Brunton , J. Nathan Kutz

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,…

Machine Learning · Computer Science 2018-10-17 Xu Feng , Wenjian Yu , Yaohang Li

In this paper, we propose new randomization based algorithms for large scale linear discrete ill-posed problems with general-form regularization: ${\min} \|Lx\|$ subject to ${\min} \|Ax - b\|$, where $L$ is a regularization matrix. Our…

Numerical Analysis · Mathematics 2019-09-24 Zhongxiao Jia , Yanfei Yang

Efficiently computing a subset of a correlation matrix consisting of values above a specified threshold is important to many practical applications. Real-world problems in genomics, machine learning, finance other applications can produce…

Computation · Statistics 2016-03-15 James Baglama , Michael Kane , Bryan Lewis , Alex Poliakov

Memristor crossbars enable vector-matrix multiplication (VMM), and are promising for low-power applications. However, it can be difficult to write the memristor conductance values exactly. To improve the accuracy of VMM, we propose a scheme…

Signal Processing · Electrical Eng. & Systems 2025-10-07 Binyu Lu , Matthias Frey , Stark Draper , Jingge Zhu