Related papers: A Sparse-Sparse Iteration for Computing a Sparse I…
We introduce a novel strategy for constructing symmetric positive definite (SPD) preconditioners for linear systems with symmetric indefinite matrices. The strategy, called absolute value preconditioning, is motivated by the observation…
Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the…
This article presents a class of modified new modulus-based iterative methods to process the large and sparse implicit complementarity problem (ICP). By using two positive diagonal matrices, we formulate a fixed-point equation which is…
In many applications, one is faced with an inverse problem, where the known signal depends in a bilinear way on two unknown input vectors. Often at least one of the input vectors is assumed to be sparse, i.e., to have only few non-zero…
In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…
We focus on inverse preconditioners based on minimizing $F(X) = 1-\cos(XA,I)$, where $XA$ is the preconditioned matrix and $A$ is symmetric and positive definite. We present and analyze gradient-type methods to minimize $F(X)$ on a suitable…
A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…
When a matrix has a banded inverse there is a remarkable formula that quickly computes that inverse, using only local information in the original matrix. This local inverse formula holds more generally, for matrices with sparsity patterns…
The recent low-rank prior based models solve the tensor completion problem efficiently. However, these models fail to exploit the local patterns of tensors, which compromises the performance of tensor completion. In this paper, we propose a…
Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample…
In this paper, we describe a new algorithm to build a few sparse principal components from a given data matrix. Our approach does not explicitly create the covariance matrix of the data and can be viewed as an extension of the Kogbetliantz…
When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is…
The convergence rate is analyzed for the SpaSRA algorithm (Sparse Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) + \psi (\m{x})$ where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth. It is shown that…
This paper introduces the sparsifying preconditioner for the pseudospectral approximation of highly indefinite systems on periodic structures, which include the frequency-domain response problems of the Helmholtz equation and the…
Nonnegative matrix factorization arises widely in machine learning and data analysis. In this paper, for a given factorization of rank r, we consider the sparse stochastic matrix factorization (SSMF) of decomposing a prescribed m-by-n…
This paper considers the problem of reconstructing sparse or compressible signals from one-bit quantized measurements. We study a new method that uses a log-sum penalty function, also referred to as the Gaussian entropy, for sparse signal…
The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite…
In this paper, we discuss numerical methods for the eigenvalue decomposition of real symmetric matrices. While many existing methods can compute approximate eigenpairs with sufficiently small backward errors, the magnitude of the resulting…
A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy a number of desirable properties. In…
Compressed sensing of simultaneously sparse and low-rank matrices enables recovery of sparse signals from a few linear measurements of their bilinear form. One important question is how many measurements are needed for a stable…