相关论文: Robust and effective eSIF preconditioning for gene…

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…

In this paper, we further investigate and refine the subspace-constrained preconditioning technique to enhance the theoretical and numerical convergence properties of randomized iterative methods for solving linear systems. In particular,…

A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schr\"odinger equations with fractional Laplacian. Complex symmetric linear systems can be obtained, and the system matrices are…

We consider symmetric positive definite preconditioners for multiple saddle-point systems of block tridiagonal form, which can be applied within the MINRES algorithm. We describe such a preconditioner for which the preconditioned matrix has…

Preconditioning is a key component of MCMC algorithms that improves sampling efficiency by facilitating exploration of geometrically complex target distributions through an invertible map. While linear preconditioners are often sufficient…

Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice,…

A modification of the generalized shift-splitting (GSS) method is presented for solving singular saddle point problems. In this kind of modification, the diagonal shift matrix is replaced by a block diagonal matrix which is symmetric…

This article introduces an iterative method for solving nonsingular non-Hermitian positive semidefinite systems of linear equations. To construct the iteration process, the coefficient matrix is split into two non-Hermitian positive…

A new domain decomposition preconditioner is introduced for efficiently solving linear systems Ax = b with a symmetric positive definite matrix A. The particularity of the new preconditioner is that it is not necessary to have access to the…

The eXtended Finite Element Method (XFEM) is an approach for solving problems with non-smooth solutions. In the XFEM, the approximate solution is locally enriched to capture discontinuities without requiring a mesh which conforms to the…

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…

With the tremendous success of large transformer models in natural language understanding, down-sizing them for cost-effective deployments has become critical. Recent studies have explored the low-rank weight factorization techniques which…

The successive projection algorithm (SPA) can quickly solve a nonnegative matrix factorization problem under a separability assumption. Even if noise is added to the problem, SPA is robust as long as the perturbations caused by the noise…

We investigate the SPAI and PSAI preconditioning procedures and shed light on two important features of them: (i) For the large linear system $Ax=b$ with $A$ irregular sparse, i.e., with $A$ having $s$ relatively dense columns, SPAI may be…

Solving the normal equations corresponding to large sparse linear least-squares problems is an important and challenging problem. For very large problems, an iterative solver is needed and, in general, a preconditioner is required to…

We present a Calder\'on preconditioning scheme for the symmetric formulation of the forward electroencephalographic (EEG) problem that cures both the dense discretization and the high-contrast breakdown. Unlike existing Calder\'on schemes…

State estimation of nonlinear dynamical systems has long aimed to balance accuracy, computational efficiency, robustness, and reliability. The rapid evolution of various industries has amplified the demand for estimation frameworks that…

We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block Gaussian elimination and additionally compress the fill-in.…

Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and…

We define the notion of effective stiffness and show that it can used to build sparsifiers, algorithms that sparsify linear systems arising from finite-element discretizations of PDEs. In particular, we show that sampling $O(n\log n)$…