Related papers: Implicit Hari--Zimmermann algorithm for the genera…
By exploiting the random sampling techniques, this paper derives an efficient randomized algorithm for computing a generalized CUR decomposition, which provides low-rank approximations of both matrices simultaneously in terms of some of…
We present a generalisation of the pseudoinverse operation to pairs of matrices, as opposed to single matrices alone. We note the fact that the Singular Value Decomposition can be used to compute the ordinary Moore-Penrose pseudoinverse. We…
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…
Recently, graphics processors (GPUs) have been increasingly leveraged in a variety of scientific computing applications. However, architectural differences between CPUs and GPUs necessitate the development of algorithms that take advantage…
Dimensionality reduction is an important preprocessing step of the hyperspectral images classification (HSI), it is inevitable task. Some methods use feature selection or extraction algorithms based on spectral and spatial information. In…
Over the past decade, various matrix completion algorithms have been developed. Thresholded singular value decomposition (SVD) is a popular technique in implementing many of them. A sizable number of studies have shown its theoretical and…
In this article we present some statistical applications of the functional singular value decomposition (FSVD). This tool allows us to decompose the sample mean of a bivariate stochastic process into components that are functions of…
We study the stochastic Riemannian gradient algorithm for matrix eigen-decomposition. The state-of-the-art stochastic Riemannian algorithm requires the learning rate to decay to zero and thus suffers from slow convergence and sub-optimal…
Analyzing complex experimental data with multiple parameters is challenging. We propose using Singular Value Decomposition (SVD) as an effective solution. This method, demonstrated through real experimental data analysis, surpasses…
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…
The incremental singular value decomposition (SVD) updates a truncated SVD as new columns arrive, replacing a single large SVD with a sequence of small ones. In floating-point arithmetic, each update multiplies the running singular basis by…
The Zippel algorithm performs a rational reconstruction of multivariate polynomials and aims specifically at the sparse case. It is applied in different fields of science, lately becoming an important step in Feynman integral reduction in…
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 studies high-dimensional regression with two-way structured data. To estimate the high-dimensional coefficient vector, we propose the generalized matrix decomposition regression (GMDR) to efficiently leverage any auxiliary…
The main objective of this work consists in analyzing sub-structuring method for the parallel solution of sparse linear systems with matrices arising from the discretization of partial differential equations such as finite element, finite…
Global Value Numbering (GVN) is an important static analysis to detect equivalent expressions in a program. We present an iterative data-flow analysis GVN algorithm in SSA for the purpose of detecting total redundancies. The central…
Support Vector Machine (SVM) is an effective model for many classification problems. However, SVM needs the solution of a quadratic program which require specialized code. In addition, SVM has many parameters, which affects the performance…
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…
Huffman compression is a statistical, lossless, data compression algorithm that compresses data by assigning variable length codes to symbols, with the more frequently appearing symbols given shorter codes than the less. This work is a…
Implicit methods and GPU parallelization are two distinct yet powerful strategies for accelerating high-order CFD algorithms. However, few studies have successfully integrated both approaches within high-speed flow solvers. The core…