Concept
Divide-and-conquer eigenvalue algorithm
Publications associées (47)
RANDOMIZED JOINT DIAGONALIZATION OF SYMMETRIC
Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD) for performing t ...
Philadelphia2024Singular quadratic eigenvalue problems: linearization and weak condition numbers
Daniel Kressner, Ivana Sain Glibic
The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are ...
SPRINGER2023The first Grushin eigenvalue on cartesian product domains
Joachim Stubbe, Luigi Provenzano, Paolo Luzzini
In this paper, we consider the first eigenvalue.1(O) of the Grushin operator.G :=.x1 + |x1|2s.x2 with Dirichlet boundary conditions on a bounded domain O of Rd = R d1+ d2. We prove that.1(O) admits a unique minimizer in the class of domains with prescribed ...
WALTER DE GRUYTER GMBH2023A fast spectral divide-and-conquer method for banded matrices
Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3):A1325-A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix with small bandwidth, w ...
WILEY2021hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES
Daniel Kressner, Stefano Massei
Matrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile tool to develop fast algorithms for addressing large-scale problems. While existing software packages for such matrices often focus on linear systems, t ...
SIAM PUBLICATIONS2020hm-toolbox: Matlab software for HODLR and HSS matrices
Daniel Kressner, Stefano Massei
Matrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile tool to develop fast algorithms for addressing large-scale problems. While existing software packages for such matrices often focus on linear systems, t ...
2019