Related papers: A Sparse-Sparse Iteration for Computing a Sparse I…
Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel…
We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
We analyze a weighted Frobenius loss for approximating symmetric positive definite matrices in the context of preconditioning iterative solvers. Unlike the standard Frobenius norm, the weighted loss penalizes error components associated…
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…
The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existence, an algorithmic approach is typically necessary to…
We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…
Nonnegative matrix factorization is a powerful technique to realize dimension reduction and pattern recognition through single-layer data representation learning. Deep learning, however, with its carefully designed hierarchical structure,…
In this paper we introduce an algebraic recursive multilevel incomplete factorization preconditioner, based on a distributed Schur complement formulation, for solving general linear systems. The novelty of the proposed method is to combine…
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…
The nonlinear (preconditioned) conjugate gradient N(P)CG method and the locally optimal (preconditioned) minimal residual LO(P)MR method, both of which are used for the iterative computation of sparse approximate inverses (SPAIs) of…
We present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the…
The paper proposes a new covariance estimator for large covariance matrices when the variables have a natural ordering. Using the Cholesky decomposition of the inverse, we impose a banded structure on the Cholesky factor, and select the…
This paper introduces and analyzes a preconditioned modified of the Hermitian and skew-Hermitian splitting (PMHSS). The large sparse continuous Sylvester equations are solved by PMHSS iterative algorithm based on nonHermitian, complex,…
The effectiveness of using model sparsity as a priori information when solving linear inverse problems is studied. We investigate the reconstruction quality of such a method in the non-idealized case and compute some typical recovery errors…
We give a new probabilistic algorithm for interpolating a "sparse" polynomial f given by a straight-line program. Our algorithm constructs an approximation f* of f, such that their difference probably has at most half the number of terms of…
Linear detectors such as zero forcing (ZF) or minimum mean square error (MMSE) are imperative for large/massive MIMO systems for both the downlink and uplink scenarios. However these linear detectors require matrix inversion which is…
We develop a method for estimating well-conditioned and sparse covariance and inverse covariance matrices from a sample of vectors drawn from a sub-gaussian distribution in high dimensional setting. The proposed estimators are obtained by…
This paper examines a general class of noisy matrix completion tasks where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is…
Recently a new adaptive path interpolation method has been developed as a simple and versatile scheme to calculate exactly the asymptotic mutual information of Bayesian inference problems defined on dense factor graphs. These include random…