Multiparameter Eigenvalue Problems and Shift-invariance
نویسندگان
چکیده
We discuss four eigenvalue problems of increasing generality and complexity: rooting a univariate polynomial, solving the polynomial problem, set multivariate polynomials multi-parameter problems. In doing so, we provide unifying framework for these problems, where exploit properties (block-) (multi-) shift-invariant subspaces use multi-dimensional realization algorithms.
منابع مشابه
Spectral asymptotics and bifurcation for nonlinear multiparameter elliptic eigenvalue problems
This paper is concerned with the nonlinear multiparameter elliptic eigenvalue problem u′′(r) + N − 1 r u′(r) + μu(r)− k ∑ i=1 λifi(u(r)) = 0, 0 < r < 1, u(r) > 0, 0 ≤ r < 1, u′(0) = 0, u(1) = 0, where N ≥ 1, k ∈ N and μ, λi ≥ 0 (1 ≤ i ≤ k) are parameters. The aim of this paper is to study the asymptotic properties of eigencurve μ(λ, α) = μ(λ1, λ2, · · · , λk, α) with emphasis on the phenomenon ...
متن کاملSpectral collocation for multiparameter eigenvalue problems arising from separable boundary value problems
In numerous science and engineering applications a partial differential equation has to be solved on some fairly regular domain that allows the use of the method of separation of variables. In several orthogonal coordinate systems separation of variables applied to the Helmholtz, Laplace, or Schrödinger equation leads to a multiparameter eigenvalue problem (MEP); important cases include Mathieu...
متن کاملPerturbation of multiparameter non-self-adjoint boundary eigenvalue problems for operator matrices
We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on the complex spectral parameter λ and on the vector of real physical parameters p. We study perturbations of semi-simple multiple eigenvalues as well as pertu...
متن کاملShift invariance and the neocognitron
-We investigate the ability of the neocognitron to perform shift-invariant pattern recognition. Both an intuitive analysis and a more formal investigation show that the performance of the neocognitron is not intrinsically shift invariant, and that certain model parameters must be chosen appropriately to obtain approximate shift invariance. It is shown how these parameters should be chosen to re...
متن کاملHarmonic Rayleigh-ritz for the Multiparameter Eigenvalue Problem
Harmonic extraction methods for the multiparameter eigenvalue problem willbe presented. These techniques are generalizations of their counterparts forthe standard and generalized eigenvalue problem. The methods aim to ap-proximate interior eigenpairs, generally more accurately than the standardextraction does. The process can be combined with any subspace expansionapproa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IFAC-PapersOnLine
سال: 2021
ISSN: ['2405-8963', '2405-8971']
DOI: https://doi.org/10.1016/j.ifacol.2021.06.071