Related papers: Block Approximation of Tall Sparse Matrices and Bl…

Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose…

Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…

We consider discretizations of the hyper-singular integral operator on closed surfaces and show that the inverses of the corresponding system matrices can be approximated by blockwise low-rank matrices at an exponential rate in the block…

A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…

The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…

Many types of pairwise interaction take the form of a fixed set of nodes with edges that appear and disappear over time. In the case of discrete-time evolution, the resulting evolving network may be represented by a time-ordered sequence of…

The block maximum method, which is widely used in extreme value analysis, uses a generalized extreme value distribution to approximate that of the maximum of m observations. The quality of this approximation depends on the value of m and…

We consider random non-normal matrices constructed by removing one row and column from samples from Dyson's circular ensembles or samples from the classical compact groups. We develop sparse matrix models whose spectral measures match these…

Several recent problems in the representation theory of finite groups require determining whether certain characters of almost simple groups belong to the principal block. Since the values of these characters are not yet known, we employ…

The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…

Low-rank approximations of data matrices are an important dimensionality reduction tool in machine learning and regression analysis. We consider the case of categorical variables, where it can be formulated as the problem of finding…

The condition number of a diagonally scaled matrix, for appropriately chosen scaling matrices, is often less than that of the original. Equilibration scales a matrix so that the scaled matrix's row and column norms are equal. Scaling can be…

We assume that every element of a matrix has a small, individual error, and model it by an external number, which is the sum of a nonstandard real number and a neutrix, the latter being a convex (external) set having the group property. The…

Absolute value linear programming problems is quite a new area of optimization problems, involving linear functions and absolute values in the description of the model. In this paper, we consider interval uncertainty of the input…

While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…

Sparse coding, which represents a data point as a sparse reconstruction code with regard to a dictionary, has been a popular data representation method. Meanwhile, in database retrieval problems, learning the ranking scores from data points…

This is the first of two papers to describe a matrix sparsification algorithm that takes a general real or complex matrix as input and produces a sparse output matrix of the same size. The non-zero entries in the output are chosen to…

We estimate the size of the spectral gap at zero for some Hermitian block matrices. Included are quasi-definite matrices, quasi-semidefinite matrices (the closure of the set of the quasi-definite matrices) and some related block matrices…

This paper deals with the numerical computation of the least singular value of a rectangular matrix $A$ relative to a pair of closed convex cones $(P,Q)$, which is defined as the optimal value of the non-convex optimization problem of…

Motivated by recommendation systems, we consider the problem of estimating block constant binary matrices (of size $m \times n$) from sparse and noisy observations. The observations are obtained from the underlying block constant matrix…