Related papers: An Efficient Batch Solver for the Singular Value D…

Singular Value Decomposition (SVD) and its close relative, Principal Component Analysis (PCA), are well-known linear matrix decomposition techniques that are widely used in applications such as dimension reduction and clustering. However,…

The power of randomized algorithms in numerical methods have led to fast solutions which use the Singular Value Decomposition (SVD) as a core routine. However, given the large data size of modern and the modest runtime of SVD, most…

Due to importance of reducing of time solution in numerical codes, we propose an algorithm for parallel LU decomposition solver for dense and sparse matrices on GPU. This algorithm is based on first bi-vectorizing a triangular matrices of…

We demonstrate a novel technique to obtain singular-value decomposition (SVD) of the coupled-cluster triple excitations amplitudes, $t_{ijk}^{abc}$. The presented method is based on the Golub-Kahan bidiagonalisation strategy and does not…

Block-tridiagonal systems are prevalent in state estimation and optimal control, and solving these systems is often the computational bottleneck. Improving the underlying solvers therefore has a direct impact on the real-time performance of…

Spectral clustering and Singular Value Decomposition (SVD) are both widely used technique for analyzing graph data. In this note, I will present their connections using simple linear algebra, aiming to provide some in-depth understanding…

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…

The increasing number of applications requiring the solution of large scale singular value problems have rekindled interest in iterative methods for the SVD. Some promising recent ad- vances in large scale iterative methods are still…

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…

We revisit the use of Stochastic Gradient Descent (SGD) for solving convex optimization problems that serve as highly popular convex relaxations for many important low-rank matrix recovery problems such as \textit{matrix completion},…

Given multiple time series data, how can we efficiently find latent patterns in an arbitrary time range? Singular value decomposition (SVD) is a crucial tool to discover hidden factors in multiple time series data, and has been used in many…

We extend the randomized singular value decomposition (SVD) algorithm \citep{Halko2011finding} to estimate the SVD of a shifted data matrix without explicitly constructing the matrix in the memory. With no loss in the accuracy of the…

Singular Value Decomposition (SVD) has become an important technique for reducing the computational burden of Vision Language Models (VLMs), which play a central role in tasks such as image captioning and visual question answering. Although…

Low-rank approximation of images via singular value decomposition is well-received in the era of big data. However, singular value decomposition (SVD) is only for order-two data, i.e., matrices. It is necessary to flatten a higher order…

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…

Storing data is particularly a challenge when dealing with image data which often involves large file sizes due to the high resolution and complexity of images. Efficient image compression algorithms are crucial to better manage data…

This paper presents a new method capable of reconstructing datasets with great precision and very low computational cost using a novel variant of the singular value decomposition (SVD) algorithm that has been named low-cost SVD (lcSVD).…

Graphics Processing Unit (GPU) computing is becoming an alternate computing platform for numerical simulations. However, it is not clear which numerical scheme will provide the highest computational efficiency for different types of…

In this paper, we address the well-known challenge in the numerical solution of time-fractional partial differential equations (TFPDEs), namely, that the dependence on all previous time levels leads to storage requirements that grow…

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…