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The Randomized Singular Value Decomposition (RSVD) is a widely used algorithm for efficiently computing low-rank approximations of large matrices, without the need to construct a full-blown SVD. Of interest, of course, is the approximation…

Numerical Analysis · Mathematics 2025-10-09 Danil Akhtiamov , Reza Ghane , Babak Hassibi

Fast computation of singular value decomposition (SVD) is of great interest in various machine learning tasks. Recently, SVD methods based on randomized linear algebra have shown significant speedup in this regime. This paper attempts to…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-06-23 Yuechao Lu , Fumihiko Ino , Yasuyuki Matsushita

Singular value decomposition (SVD) is one of the most popular compression methods that approximate a target matrix with smaller matrices. However, standard SVD treats the parameters within the matrix with equal importance, which is a simple…

Computation and Language · Computer Science 2022-12-19 Ting Hua , Yen-Chang Hsu , Felicity Wang , Qian Lou , Yilin Shen , Hongxia Jin

In this paper, we present a natural implementation of singular value decomposition (SVD) and polar decomposition of an arbitrary multivector in nondegenerate real and complexified Clifford geometric algebras of arbitrary dimension and…

Mathematical Physics · Physics 2024-12-24 D. S. Shirokov

Singular value decomposition (SVD) is a widely used technique for dimensionality reduction and computation of basis vectors. In many applications, especially in fluid mechanics and image processing the matrices are dense, but low-rank…

Numerical Analysis · Computer Science 2019-05-13 Vinita Vasudevan , M. Ramakrishna

By singular value decomposition (SVD) of a numerically singular Hessian matrix and a numerically singular system of linear equations for the experimental data (accumulated in the respective ${\chi ^2}$ function) and constraints, least…

High Energy Physics - Phenomenology · Physics 2014-08-27 Mehrdad Goshtasbpour

Singular Spectrum Analysis (SSA) or Singular Value Decomposition (SVD) are often used to de-noise univariate time series or to study their spectral profile. Both techniques rely on the eigendecomposition of the cor- relation matrix…

Signal Processing · Electrical Eng. & Systems 2018-07-30 A. M. Tomé , D. Malafaia , A. R. Teixeira , E. W. Lang

A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any…

Numerical Analysis · Mathematics 2014-08-12 Ming Gu

The success of matrix factorizations such as the singular value decomposition (SVD) has motivated the search for even more factorizations. We catalog 53 matrix factorizations, most of which we believe to be new. Our systematic approach,…

Numerical Analysis · Mathematics 2022-02-15 Alan Edelman , Sungwoo Jeong

The singular value decomposition (SVD) is a widely used matrix factorization tool which underlies plenty of useful applications, e.g. recommendation system, abnormal detection and data compression. Under the environment of emerging Internet…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-03-23 Shuo Chen , Rongxing Lu , Jie Zhang

We revisit a singular value decomposition (SVD) algorithm given in Chen et al. (2019b) for exploratory Item Factor Analysis (IFA). This algorithm estimates a multidimensional IFA model by SVD and was used to obtain a starting point for…

Methodology · Statistics 2025-01-08 Haoran Zhang , Yunxiao Chen , Xiaoou Li

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…

Numerical Analysis · Computer Science 2017-04-20 Yaohang Li , Wenjian Yu

This paper discusses clustering and latent semantic indexing (LSI) aspects of the singular value decomposition (SVD). The purpose of this paper is twofold. The first is to give an explanation on how and why the singular vectors can be used…

Machine Learning · Computer Science 2012-11-19 Andri Mirzal

The randomized singular value decomposition (R-SVD) is a popular sketching-based algorithm for efficiently computing the partial SVD of a large matrix. When the matrix is low-rank, the R-SVD produces its partial SVD exactly; but when the…

Information Theory · Computer Science 2023-07-07 Elad Romanov

In signal processing and identification, generalized singular value decomposition (GSVD), related to a sequence of matrices in product/quotient form are essential numerical linear algebra tools. On behalf of the growing demand for efficient…

Numerical Analysis · Mathematics 2025-11-13 Sitao Ling , Wenxuan Ma , Musheng Wei

Distributions measured in high energy physics experiments are usually distorted and/or transformed by various detector effects. A regularization method for unfolding these distributions is re-formulated in terms of the Singular Value…

High Energy Physics - Phenomenology · Physics 2008-11-26 Andreas Hoecker , Vakhtang Kartvelishvili

BACKGROUND. Formal demography has a long history of building simple models of age schedules of demographic quantities, e.g. mortality and fertility rates. These are widely used in demographic methods to manipulate whole age schedules using…

Applications · Statistics 2015-04-09 Samuel J. Clark

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

Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although…

Quantum Physics · Physics 2021-06-30 Xin Wang , Zhixin Song , Youle Wang

Singular Value Decomposition (SVD) constitutes a bridge between the linear algebra concepts and multi-layer neural networks---it is their linear analogy. Besides of this insight, it can be used as a good initial guess for the network…

Machine Learning · Computer Science 2019-09-16 Bernhard Bermeitinger , Tomas Hrycej , Siegfried Handschuh