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Singular Value Decomposition (SVD) is a well studied research topic in many fields and applications from data mining to image processing. Data arising from these applications can be represented as a matrix where it is large and sparse. Most…
The singular value decomposition (SVD) allows to write a matrix as a product of a left singular vectors matrix, a nonnegative singular values diagonal matrix and a right singular vectors matrix. Among the applications of the SVD are the…
Singular Value Decomposition (SVD) is one of the most useful techniques for analyzing data in linear algebra. SVD decomposes a rectangular real or complex matrix into two orthogonal matrices and one diagonal matrix. In this work we…
We propose new algorithms for singular value decomposition (SVD) of very large-scale matrices based on a low-rank tensor approximation technique called the tensor train (TT) format. The proposed algorithms can compute several dominant…
In this paper a vectorized algorithm for simultaneously computing up to eight singular value decompositions (SVDs, each of the form $A=U\Sigma V^{\ast}$) of real or complex matrices of order two is proposed. The algorithm extends to a batch…
With the abundance of data in recent years, interesting challenges are posed in the area of recommender systems. Producing high quality recommendations with scalability and performance is the need of the hour. Singular Value…
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…
A one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, using a massively parallel graphics processing unit (GPU), is developed. The algorithm also serves as the final stage of solving a symmetric indefinite eigenvalue…
The singular value decomposition (SVD) is not only a classical theory in matrix computation and analysis, but also is a powerful tool in machine learning and modern data analysis. In this tutorial we first study the basic notion of SVD and…
We present high performance implementations of the QR and the singular value decomposition of a batch of small matrices hosted on the GPU with applications in the compression of hierarchical matrices. The one-sided Jacobi algorithm is used…
Quantum-inspired singular value decomposition (SVD) is a technique to perform SVD in logarithmic time with respect to the dimension of a matrix, given access to the matrix embedded in a segment-tree data structure. The speedup is possible…
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…
A parallel, blocked, one-sided Hari--Zimmermann algorithm for the generalized singular value decomposition (GSVD) of a real or a complex matrix pair $(F,G)$ is here proposed, where $F$ and $G$ have the same number of columns, and are both…
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…
Singular value decomposition (SVD) and matrix inversion are ubiquitous in scientific computing. Both tasks are computationally demanding for large scale matrices. Existing algorithms can approximatively solve these problems with a given…
Aiming to provide a faster and convenient truncated SVD algorithm for large sparse matrices from real applications (i.e. for computing a few of largest singular values and the corresponding singular vectors), a dynamically shifted power…
Three refined and refined harmonic extraction-based Jacobi--Davidson (JD) type methods are proposed, and their thick-restart algorithms with deflation and purgation are developed to compute several generalized singular value decomposition…
In this paper, we show that the SVD of a matrix can be constructed efficiently in a hierarchical approach. Our algorithm is proven to recover the singular values and left singular vectors if the rank of the input matrix $A$ is known.…
This paper develops fast and efficient algorithms for computing Tucker decomposition with a given multilinear rank. By combining random projection and the power scheme, we propose two efficient randomized versions for the truncated…
This paper presents a portable, GPU-accelerated implementation of a QR-based singular value computation algorithm in Julia. The singular value ecomposition (SVD) is a fundamental numerical tool in scientific computing and machine learning,…