Related papers: Adaptive Parallelizable Algorithms for Interpolati…

The CANDECOMP/PARAFAC (CP) decomposition is a leading method for the analysis of multiway data. The standard alternating least squares algorithm for the CP decomposition (CP-ALS) involves a series of highly overdetermined linear least…

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…

A general framework for solving the subspace clustering problem using the CUR decomposition is presented. The CUR decomposition provides a natural way to construct similarity matrices for data that come from a union of unknown subspaces…

Large deep learning models have achieved remarkable success but are resource-intensive, posing challenges such as memory usage. We introduce CURing, a novel model compression method based on CUR matrix decomposition, which approximates…

We develop the symplectic elimnation algorithm. This algorithm using simple row operations reduce a symplectic matrix to a diagonal matrix. This algorithm gives rise to a decomposition of an arbitrary matrix into a product of a symplectic…

Structured pruning is a commonly used convolutional neural network (CNN) compression approach. Pruning rate setting is a fundamental problem in structured pruning. Most existing works introduce too many additional learnable parameters to…

Transforming a matrix over a field to echelon form, or decomposing the matrix as a product of structured matrices that reveal the rank profile, is a fundamental building block of computational exact linear algebra. This paper surveys the…

Column-pivoted QR (CPQR) factorization is a computational primitive used in numerous applications that require selecting a small set of ``representative'' columns from a much larger matrix. These include applications in spectral clustering,…

While there exists a rich array of matrix column subset selection problem (CSSP) algorithms for use with interpolative and CUR-type decompositions, their use can often become prohibitive as the size of the input matrix increases. In an…

This paper describes efficient algorithms for computing rank-revealing factorizations of matrices that are too large to fit in RAM, and must instead be stored on slow external memory devices such as solid-state or spinning disk hard drives…

Non-regular sampling can reduce aliasing at the expense of noise. Recently, it has been shown that non-regular sampling can be carried out using a conventional regular imaging sensor when the surface of its individual pixels is partially…

CUR and low-rank approximations are among most fundamental subjects of numerical linear algebra, with a wide range of applications to a variety of highly important areas of modern computing, which range from the machine learning theory and…

The CP tensor decomposition is a low-rank approximation of a tensor. We present a distributed-memory parallel algorithm and implementation of an alternating optimization method for computing a CP decomposition of dense tensor data that can…

Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…

We present Flip-Flop Spectrum-Revealing QR (Flip-Flop SRQR) factorization, a significantly faster and more reliable variant of the QLP factorization of Stewart, for low-rank matrix approximations. Flip-Flop SRQR uses SRQR factorization to…

Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning. In theory, under certain conditions, this problem can be…

There are variety of computational algorithms need sequential sweeping; sweeping based on specific order; on a structured grid, e.g., preconditioning (smoothing) by SOR or ILU methods and solution of eikonal equation by fast sweeping…

We tackle the problem of graph partitioning for image segmentation using correlation clustering (CC), which we treat as an integer linear program (ILP). We reformulate optimization in the ILP so as to admit efficient optimization via…

This paper introduces fast R updating algorithms specifically designed for statistical applications, including regression, filtering, and model selection, where data structures change frequently. Although traditional QR decomposition is…

With the increasing popularity of deep learning in image processing, many learned lossless image compression methods have been proposed recently. One group of algorithms that have shown good performance are based on learned pixel-based…