相关论文: ARAS: Fully algebraic Two-level domain decompositi…

Convergence of domain decomposition methods rely heavily on the efficiency of the coarse space used in the second level. The GenEO coarse space has been shown to lead to a fully robust two-level Schwarz preconditioner which scales well over…

In the present study, we consider the numerical method for Toeplitz-like linear systems arising from the $d$-dimensional Riesz space fractional diffusion equations (RSFDEs). We apply the Crank-Nicolson (CN) technique to discretize the…

In this paper, a compact alternating direction implicit (ADI) method has been developed for solving two-dimensional Riesz space fractional diffusion equation. The precision of the discretization method used in spatial directions is twice…

This paper introduces a robust preconditioner for general sparse symmetric matrices, that is based on low-rank approximations of the Schur complement in a Domain Decomposition (DD) framework. In this "Schur Low Rank" (SLR) preconditioning…

Statistical preconditioning enables fast methods for distributed large-scale empirical risk minimization problems. In this approach, multiple worker nodes compute gradients in parallel, which are then used by the central node to update the…

Domain decomposition (DD) methods are widely used as preconditioner techniques. Their effectiveness relies on the choice of a locally constructed coarse space. Thus far, this construction was mostly achieved using non-assembled matrices…

We deal with the numerical solution of the time-dependent partial differential equations using the adaptive space-time discontinuous Galerkin (DG) method. The discretization leads to a nonlinear algebraic system at each time level, the size…

The complex-shifted Laplacian systems arising in a wide range of applications. In this work, we propose an absolute-value based preconditioner for solving the complex-shifted Laplacian system. In our approach, the complex-shifted Laplacian…

Since reconfigurable intelligent surface (RIS) is considered to be a passive reflector for rate performance enhancement, a RIS-aided amplify-and-forward (AF) relay network is presented. By jointly optimizing the beamforming matrix at AF…

We present a stationary iteration method, namely Alternating Symmetric positive definite and Scaled symmetric positive semidefinite Splitting (ASSS), for solving the system of linear equations obtained by using finite element discretization…

Diffusion models (DMs) have become the leading choice for generative tasks across diverse domains. However, their reliance on multiple sequential forward passes significantly limits real-time performance. Previous acceleration methods have…

Inference-time scaling can reduce errors in structured query generation, but methods to allocate the compute for query code generation remains underexplored. We study Text2Cypher, where language models generate Cypher queries that execute…

Efficient algorithms for the solution of partial differential equations on parallel computers are often based on domain decomposition methods. Schwarz preconditioners combined with standard Krylov space solvers are widely used in this…

We consider one-level additive Schwarz preconditioners for a family of Helmholtz problems with absorption and increasing wavenumber $k$. These problems are discretized using the Galerkin method with nodal conforming finite elements of any…

This Paper conducts a thorough simulation study to assess the effectiveness of various acceleration techniques designed to enhance the conjugate gradient algorithm, which is used for solving large linear systems to accelerate Bayesian…

Auto-Regressive (AR) models have recently gained prominence in image generation, often matching or even surpassing the performance of diffusion models. However, one major limitation of AR models is their sequential nature, which processes…

Solving optimization problems with transient PDE-constraints is computationally costly due to the number of nonlinear iterations and the cost of solving large-scale KKT matrices. These matrices scale with the size of the spatial…

Markov Random Fields (MRFs) are a popular model for several pattern recognition and reconstruction problems in robotics and computer vision. Inference in MRFs is intractable in general and related work resorts to approximation algorithms.…

In this paper, we propose a speed-up approach for subclass discriminant analysis and formulate a novel efficient multi-view solution to it. The speed-up approach is developed based on graph embedding and spectral regression approaches that…

This paper presents estimates of the convergence rate and complexity of an algebraic multilevel preconditioner based on piecewise constant coarse vector spaces applied to the graph Laplacian. A bound is derived on the energy norm of the…