相关论文: Approximate multiplication of nearly sparse matric…
Artificial intelligence workloads, especially transformer models, exhibit emergent sparsity in which computations perform selective sparse access to dense data. The workloads are inefficient on hardware designed for dense computations and…
We introduce a task-parallel algorithm for sparse incomplete Cholesky factorization that utilizes a 2D sparse partitioned-block layout of a matrix. Our factorization algorithm follows the idea of algorithms-by-blocks by using the block…
We introduce a novel algorithm that computes the $k$-sparse principal component of a positive semidefinite matrix $A$. Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a low-dimensional…
We derive analytical expression of matrix factorization/completion solution by variational Bayes method, under the assumption that observed matrix is originally the product of low-rank dense and sparse matrices with additive noise. We…
In this paper, we show a way to exploit sparsity in the problem data in a primal-dual potential reduction method for solving a class of semidefinite programs. When the problem data is sparse, the dual variable is also sparse, but the primal…
Although reliable long precision floating-point arithmetic libraries such as QD and MPFR/GMP are necessary to solve ill-conditioned problems in numerical simulation, long precision BLAS-level computation such as matrix multiplication has…
The need for fast sparse optimization is emerging, e.g., to deal with large-dimensional data-driven problems and to track time-varying systems. In the framework of linear sparse optimization, the iterative shrinkage-thresholding algorithm…
To obtain accurate results in numerical computation, high-precision arithmetic is a straightforward approach. However, most processors lack hardware support for floating-point formats beyond double precision (FP64). Double-word arithmetic…
Sparse approximations using highly over-complete dictionaries is a state-of-the-art tool for many imaging applications including denoising, super-resolution, compressive sensing, light-field analysis, and object recognition. Unfortunately,…
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…
Our main interest in this paper is to study some approximation problems for classes of functions with mixed smoothness. We use technique, based on a combination of results from hyperbolic cross approximation, which were obtained in 1980s --…
With the commercial availability of mixed precision hardware, mixed precision GMRES-based iterative refinement schemes have emerged as popular approaches for solving sparse linear systems. Existing analyses of these approaches, however, are…
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…
The emergence of low precision floating-point arithmetic in computer hardware has led to a resurgence of interest in the use of mixed precision numerical linear algebra. For linear systems of equations, there has been renewed enthusiasm for…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
We present a method for parallel block-sparse matrix-matrix multiplication on distributed memory clusters. By using a quadtree matrix representation, data locality is exploited without prior information about the matrix sparsity pattern. A…
Finding the product of two polynomials is an essential and basic problem in computer algebra. While most previous results have focused on the worst-case complexity, we instead employ the technique of adaptive analysis to give an improvement…
Given a redundant dictionary $\Phi$, represented by an $M \times N$ matrix ($\Phi \in \mathbb{R}^{M \times N}$) and a target signal $y \in \mathbb{R}^M$, the \emph{sparse approximation problem} asks to find an approximate representation of…
We consider the problem of computing an approximate banded solution of the continuous-time Lyapunov equation $\underline{A}\underline{X}+\underline{X}\underline{A}^{T}=\underline{P}$, where the coefficient matrices $\underline{A}$ and…
In this paper, we consider the matrices approximated in H2 format. The direct solution, as well as the preconditioning, of systems with such matrices is a challenging problem. We propose a non-extensive sparse factorization of the H2 matrix…