Zobrazeno 1 - 10
of 195
pro vyhledávání: '"Martinsson, Per"'
Solving very large linear systems of equations is a key computational task in science and technology. In many cases, the coefficient matrix of the linear system is rank-deficient, leading to systems that may be underdetermined, inconsistent, or both.
Externí odkaz:
http://arxiv.org/abs/2408.05238
The hierarchical matrix ($\mathcal{H}^{2}$-matrix) formalism provides a way to reinterpret the Fast Multipole Method and related fast summation schemes in linear algebraic terms. The idea is to tessellate a matrix into blocks in such as way that each
Externí odkaz:
http://arxiv.org/abs/2311.01451
This work introduces the kernel-independent multi-level algorithm "skelFMM" for evaluating all pairwise interactions between $N$ points connected through a kernel such as the fundamental solution of the Laplace or the Helmholtz equations. The method
Externí odkaz:
http://arxiv.org/abs/2310.16668
Boundary value problems involving elliptic PDEs such as the Laplace and the Helmholtz equations are ubiquitous in mathematical physics and engineering. Many such problems can be alternatively formulated as integral equations that are mathematically m
Externí odkaz:
http://arxiv.org/abs/2310.15458
Interpolative and CUR decompositions involve "natural bases" of row and column subsets, or skeletons, of a given matrix that approximately span its row and column spaces. These low-rank decompositions preserve properties such as sparsity or non-negat
Externí odkaz:
http://arxiv.org/abs/2310.09417
The interpolative decomposition (ID) aims to construct a low-rank approximation formed by a basis consisting of row/column skeletons in the original matrix and a corresponding interpolation matrix. This work explores fast and accurate ID algorithms f
Externí odkaz:
http://arxiv.org/abs/2309.16002
An additive Runge-Kutta method is used for the time stepping, which integrates the linear stiff terms by an explicit singly diagonally implicit Runge-Kutta (ESDIRK) method and the nonlinear terms by an explicit Runge-Kutta (ERK) method. In each time
Externí odkaz:
http://arxiv.org/abs/2306.02526
Parallel optimizations for the 2D Hierarchical Poincar\'e-Steklov (HPS) discretization scheme are described. HPS is a multi-domain spectral collocation scheme that allows for combining very high order discretizations with direct solvers, making the d
Externí odkaz:
http://arxiv.org/abs/2211.14969
The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a two dimensional domain. The solver is designed to reduce communication costs and perform well on GPUs; it uses a two-level fr
Externí odkaz:
http://arxiv.org/abs/2211.07572
Randomized subspace approximation with "matrix sketching" is an effective approach for constructing approximate partial singular value decompositions (SVDs) of large matrices. The performance of such techniques has been extensively analyzed, and very
Externí odkaz:
http://arxiv.org/abs/2211.04676