Zobrazeno 1 - 10
of 548
pro vyhledávání: '"KRESSNER, DANIEL"'
Preconditioned eigenvalue solvers offer the possibility to incorporate preconditioners for the solution of large-scale eigenvalue problems, as they arise from the discretization of partial differential equations. The convergence analysis of such meth
Externí odkaz:
http://arxiv.org/abs/2412.14665
Autor:
Cortinovis, Alice, Kressner, Daniel
We derive a new adaptive leverage score sampling strategy for solving the Column Subset Selection Problem (CSSP). The resulting algorithm, called Adaptive Randomized Pivoting, can be viewed as a randomization of Osinsky's recently proposed determinis
Externí odkaz:
http://arxiv.org/abs/2412.13992
This work proposes and analyzes a new class of numerical integrators for computing low-rank approximations to solutions of matrix differential equation. We combine an explicit Runge-Kutta method with repeated randomized low-rank approximation to keep
Externí odkaz:
http://arxiv.org/abs/2409.06384
Publikováno v:
Numerical Algorithms (2024)
It is well known that a family of $n\times n$ commuting matrices can be simultaneously triangularized by a unitary similarity transformation. The diagonal entries of the triangular matrices define the $n$ joint eigenvalues of the family. In this work
Externí odkaz:
http://arxiv.org/abs/2409.00500
This work is concerned with the numerical solution of large-scale symmetric positive definite matrix equations of the form $A_1XB_1^\top + A_2XB_2^\top + \dots + A_\ell X B_\ell^\top = F$, as they arise from discretized partial differential equations
Externí odkaz:
http://arxiv.org/abs/2408.16416
Autor:
Kressner, Daniel, Shao, Nian
Computing the null space of a large sparse matrix $A$ is a challenging computational problem, especially if the nullity -- the dimension of the null space -- is large. When using a block Lanczos method for this purpose, conventional wisdom suggests t
Externí odkaz:
http://arxiv.org/abs/2407.04634
Autor:
He, Haoze, Kressner, Daniel
We present and analyze a simple numerical method that diagonalizes a complex normal matrix A by diagonalizing the Hermitian matrix obtained from a random linear combination of the Hermitian and skew-Hermitian parts of A.
Externí odkaz:
http://arxiv.org/abs/2405.18399
Various iterative eigenvalue solvers have been developed to compute parts of the spectrum for a large sparse matrix, including the power method, Krylov subspace methods, contour integral methods, and preconditioned solvers such as the so called LOBPC
Externí odkaz:
http://arxiv.org/abs/2405.11962
Compactly representing and efficently applying linear operators are fundamental ingredients in tensor network methods for simulating quantum many-body problems and solving high-dimensional problems in scientific computing. In this work, we study such
Externí odkaz:
http://arxiv.org/abs/2405.09952
The randomized singular value decomposition (SVD) has become a popular approach to computing cheap, yet accurate, low-rank approximations to matrices due to its efficiency and strong theoretical guarantees. Recent work by Boull\'e and Townsend (FoCM,
Externí odkaz:
http://arxiv.org/abs/2404.00960