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Eigenvalues of parameter-dependent quadratic eigenvalue problems form eigencurves. The critical points on these curves, where the derivative vanishes, are of practical interest. A particular example is found in the dispersion curves of elastic wavegu
Externí odkaz:
http://arxiv.org/abs/2411.09584
Autor:
Plestenjak, Bor
We investigate critical points of eigencurves of bivariate matrix pencils $A+\lambda B +\mu C$. Points $(\lambda,\mu)$ for which $\det(A+\lambda B+\mu C)=0$ form algebraic curves in $\mathbb C^2$ and we focus on points where $\mu'(\lambda)=0$. Such p
Externí odkaz:
http://arxiv.org/abs/2411.07450
Autor:
Stewart, Michael
Publikováno v:
SIAM Journal on Matrix Analysis and Applications Vol. 45, No. 3, pp. 1392-1413, 2024
The spectral transformation Lanczos method for the sparse symmetric definite generalized eigenvalue problem for matrices $A$ and $B$ is an iterative method that addresses the case of semidefinite or ill conditioned $B$ using a shifted and inverted fo
Externí odkaz:
http://arxiv.org/abs/2411.03534
Mass scaling is widely used in finite element models of structural dynamics for increasing the critical time step of explicit time integration methods. While the field has been flourishing over the years, it still lacks a strong theoretical basis and
Externí odkaz:
http://arxiv.org/abs/2410.23816
Autor:
Sobczyk, Aleksandros
In this work we revisit the arithmetic and bit complexity of Hermitian eigenproblems. We first provide an analysis for the divide-and-conquer tridiagonal eigensolver of Gu and Eisenstat [GE95] in the Real RAM model, when accelerated with the Fast Mul
Externí odkaz:
http://arxiv.org/abs/2410.21550
In this paper we propose and analyze an algorithm for identifying spectral gaps of a real symmetric matrix $A$ by simultaneously approximating the traces of spectral projectors associated with multiple different spectral slices. Our method utilizes H
Externí odkaz:
http://arxiv.org/abs/2410.15349
Autor:
Mataigne, Simon, Gallivan, Kyle A.
We propose a fast method for computing the eigenvalue decomposition of a dense real normal matrix $A$. The method leverages algorithms that are known to be efficiently implemented, such as the bidiagonal singular value decomposition and the symmetric
Externí odkaz:
http://arxiv.org/abs/2410.12421
For the generalized eigenvalue problem, a quotient function is devised for estimating eigenvalues in terms of an approximate eigenvector. This gives rise to an infinite family of quotients, all entirely arguable to be used in estimation. Although the
Externí odkaz:
http://arxiv.org/abs/2409.14790
Given (orthonormal) approximations $\tilde{U}$ and $\tilde{V}$ to the left and right subspaces spanned by the leading singular vectors of a matrix $A$, we discuss methods to approximate the leading singular values of $A$ and study their accuracy. In
Externí odkaz:
http://arxiv.org/abs/2409.09187
We consider the approximation of the smallest eigenvalue of a large parameter-dependent Hermitian matrix over a continuum compact domain. Our approach is based on approximating the smallest eigenvalue by the one obtained by projecting the large matri
Externí odkaz:
http://arxiv.org/abs/2409.05791