Related papers: Localized inverse factorization
This paper elaborates on a sieving technique that has first been applied in 2018 for improving bounds on deterministic integer factorization. We will generalize the sieve in order to obtain a polynomial-time reduction from integer…
We introduce efficient $(1+\varepsilon)$-approximation algorithms for the binary matrix factorization (BMF) problem, where the inputs are a matrix $\mathbf{A}\in\{0,1\}^{n\times d}$, a rank parameter $k>0$, as well as an accuracy parameter…
Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and…
Low-latency gravitational wave search pipelines such as GstLAL take advantage of low-rank factorization of the template matrix via singular value decomposition (SVD). With unprecedented improvements in detector bandwidth and sensitivity in…
An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4} -inverses and the Moore-Penrose inverse of a given rational matrix A is established. Classes A(2, 3)s and A(2, 4)s are characterized in terms of matrix products (R*A)+R* and…
We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For…
We conduct a study and comparison of superiorization and optimization approaches for the reconstruction problem of superiorized/regularized least-squares solutions of underdetermined linear equations with nonnegativity variable bounds.…
Optimization problems over permutation matrices appear widely in facility layout, chip design, scheduling, pattern recognition, computer vision, graph matching, etc. Since this problem is NP-hard due to the combinatorial nature of…
In binary polynomial optimization, the goal is to find a binary point maximizing a given polynomial function. In this paper, we propose a novel way of formulating this general optimization problem, which we call factorized binary polynomial…
A new scaling and recovering algorithm is proposed for simultaneously computing the matrix $\varphi$-functions that arise in exponential integrator methods for the numerical solution of certain first-order systems of ordinary differential…
Affine rank minimization algorithms typically rely on calculating the gradient of a data error followed by a singular value decomposition at every iteration. Because these two steps are expensive, heuristic approximations are often used to…
The sparse factorization of a large matrix is fundamental in modern statistical learning. In particular, the sparse singular value decomposition and its variants have been utilized in multivariate regression, factor analysis, biclustering,…
This letter proposes the inverse LDM' and LU factorizations of a matrix partitioned into 2x2 blocks, which include the square-root and division free version. The proposed squareroot and division free inverse LDM' factorization is applied to…
A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any…
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…
We present an approach to decomposition and factor analysis of matrices with ordinal data. The matrix entries are grades to which objects represented by rows satisfy attributes represented by columns, e.g. grades to which an image is red, a…
We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the…
In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…
Binary matrix factorisation is an essential tool for identifying discrete patterns in binary data. In this paper we consider the rank-k binary matrix factorisation problem (k-BMF) under Boolean arithmetic: we are given an n x m binary…
The high computational cost involved in modeling of the progressive fracture simulations using large discrete lattice networks stems from the requirement to solve {\it a new large set of linear equations} every time a new lattice bond is…