相关论文: An Approach to Making SPAI and PSAI Preconditionin…

In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…

In this article, we introduce a three-precision formulation of the General Alternating-Direction Implicit method (GADI) designed to accelerate the solution of large-scale sparse linear systems $Ax=b$. GADI is a framework that can represent…

This paper investigates a type of fast and flexible preconditioners to solve multilinear system $\mathcal{A}\textbf{x}^{m-1}=\textbf{b}$ with $\mathcal{M}$-tensor $\mathcal{A}$ and obtains some important convergent theorems about…

We derive fundamental sample complexity bounds for recovering sparse and structured signals for linear and nonlinear observation models including sparse regression, group testing, multivariate regression and problems with missing features.…

Posterior sampling with the spike-and-slab prior [MB88], a popular multimodal distribution used to model uncertainty in variable selection, is considered the theoretical gold standard method for Bayesian sparse linear regression [CPS09,…

Domain decomposition methods are among the most efficient for solving sparse linear systems of equations. Their effectiveness relies on a judiciously chosen coarse space. Originally introduced and theoretically proved to be efficient for…

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…

This paper introduces a fully algebraic two-level additive Schwarz preconditioner for general sparse large-scale matrices. The preconditioner is analyzed for symmetric positive definite (SPD) matrices. For those matrices, the coarse space…

We present an efficient preconditioner for linear problems $A x=y$. It guarantees monotonic convergence of the memory-efficient fixed-point iteration for all accretive systems of the form $A = L + V$, where $L$ is an approximation of $A$,…

Can linear systems be solved faster than matrix multiplication? While there has been remarkable progress for the special cases of graph structured linear systems, in the general setting, the bit complexity of solving an $n \times n$ linear…

Large Language Models (LLMs) are difficult to fully fine-tune (e.g., with instructions or human feedback) due to their sheer number of parameters. A family of parameter-efficient sparse fine-tuning methods have proven promising in terms of…

Motivated by recent progress on stochastic matching with few queries, we embark on a systematic study of the sparsification of stochastic packing problems (SPP) more generally. Specifically, we consider SPPs where elements are independently…

In this paper, we analyze different preconditionings designed to enhance robustness of pure-pixel search algorithms, which are used for blind hyperspectral unmixing and which are equivalent to near-separable nonnegative matrix factorization…

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…

Sparse deep neural networks have proven to be efficient for predictive model building in large-scale studies. Although several works have studied theoretical and numerical properties of sparse neural architectures, they have primarily…

In this paper, the concept of matrix splitting is introduced to solve a large sparse ill-posed linear system via Tikhonov's regularization. In the regularization process, we convert the ill-posed system to a well-posed system. The…

Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with…

Affine variational inequalities (AVI) are an important problem class that generalize systems of linear equations, linear complementarity problems and optimality conditions for quadratic programs. This paper describes PATHAVI, a…

In this paper we study fast iterative solvers for the large sparse linear systems resulting from the stochastic Galerkin discretization of stochastic partial differential equations. A block triangular preconditioner is introduced and…

Polynomial approximations of computationally intensive models are central to uncertainty quantification. This paper describes an adaptive method for non-intrusive pseudospectral approximation, based on Smolyak's algorithm with generalized…