Related papers: Mixed precision thin SVD algorithms based on the G…

This paper aims at a better understanding of matrix factorization (MF), factorization machines (FM), and their combination with deep algorithms' application in recommendation systems. Specifically, this paper will focus on Singular Value…

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…

This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality…

The paper presents a new Kalman filter (KF) implementation useful in applications where the accuracy of numerical solution of the associated Riccati equation might be crucially reduced by influence of roundoff errors. Since the appearance…

Singular Value Decomposition (SVD) is a powerful tool in linear algebra.We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The paper illustrates nonlinear SVD…

We evaluate performance of associative memory in a neural network by based on the singular value decomposition (SVD) of image data stored in the network. We consider the situation in which the original image and its highly coarse-grained…

The Singular Value Decomposition is a matrix decomposition technique widely used in the analysis of multivariate data, such as complex space-time images obtained in both physical and biological systems. In this paper, we examine the…

We make a convergence analysis of the harmonic and refined harmonic extraction versions of Jacobi-Davidson SVD (JDSVD) type methods for computing one or more interior singular triplets of a large matrix $A$. At each outer iteration of these…

We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…

Matrix multiplication computation acceleration has been a research hotspot across various domains. Due to the characteristics of some applications, approximate matrix multiplication can achieve significant performance improvements without…

We consider the solution of the Sylvester equation $AX+XB=C$ in mixed precision. We derive a new iterative refinement scheme to solve perturbed quasi-triangular Sylvester equations; our rounding error analysis provides sufficient conditions…

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…

This paper gives a new scheme of colour image compression related to singular values matrix approximation. The image has to be converted in luminance / chrominance space before being processed like JPEG standard 4 : 2 : 0. Our approach is…

The hierarchical SVD provides a quasi-best low rank approximation of high dimensional data in the hierarchical Tucker framework. Similar to the SVD for matrices, it provides a fundamental but expensive tool for tensor computations. In the…

Low-rank decomposition, particularly Singular Value Decomposition (SVD), is a pivotal technique for mitigating the storage and computational demands of Large Language Models (LLMs). However, prevalent SVD-based approaches overlook the…

This paper aims to develop a simple procedure to reduce and control the condition number of random matrices, and investigate the effect on the persistent homology (PH) of point clouds of well- and ill-conditioned matrices. For a square…

We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…

The oriented singular value decomposition (O-SVD) proposed by Zeng and Ng provides a hybrid approach to the t-product based third-order tensor singular value decomposition with the transform matrix being a factor matrix of the higher order…

The massive scale of pretrained models has made efficient compression essential for practical deployment. Low-rank decomposition based on the singular value decomposition (SVD) provides a principled approach for model reduction, but its…

This work deals with developing two fast randomized algorithms for computing the generalized tensor singular value decomposition (GTSVD) based on the tubal product (t-product). The random projection method is utilized to compute the…