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Kernel polynomials from L-orthogonal polynomials
(2011-05-01)
A positive measure ψ defined on [a,b] such that its moments μn=∫a btndψ(t) exist for n=0,±1,±2,⋯, is called a strong positive measure on [a,b]. If 0≤a<b≤∞ then the sequence of (monic) polynomials {Qn}, defined by ∫a ...
Kernel polynomials from L-orthogonal polynomials
(2011-05-01)
A positive measure ψ defined on [a,b] such that its moments μn=∫a btndψ(t) exist for n=0,±1,±2,⋯, is called a strong positive measure on [a,b]. If 0≤a<b≤∞ then the sequence of (monic) polynomials {Qn}, defined by ∫a ...
The inverse eigenvalue problem for a Hermitian reflexive matrix and the optimization problem
The inverse eigenvalue problem and the associated optimal approximation problem for Hermitian reflexive matrices with respect to a normal {k+1}-potent matrix are considered. First, we study the existence of the solutions ...
Eigenvalue problems in a non-Lipschitz domain
(Oxford University Press, 2013-05)
In this paper we analyse piecewise linear finite element approximations of the Laplace eigenvalue problem in the plane domain Ω = { (x,y) : 0 < x < 1 , 0 < y < xα}, which gives for 1<α the simplest model of an external ...
Neural network solution for an inverse problem associated with the dirichlet eigenvalues of the anisotropic laplace operator
(2016)
An innovative numerical method based on an artificial neural network is presented in order to solve an inverse problem associated with the calculation of the Dirichlet eigenvalues of the anisotropic Laplace operator. Using ...
R II type recurrence, generalized eigenvalue problem and orthogonal polynomials on the unit circle
(2019-02-01)
We consider a sequence of polynomials {P n } n≥0 satisfying a special R II type recurrence relation where the zeros of P n are simple and lie on the real line. It turns out that the polynomial P n , for any n≥2, is the ...
An Efficient Galerkin BEM to Compute High Acoustic Eigenfrequencies
(ASME-AMER SOC MECHANICAL ENG, 2009)
An efficient numerical method, using integral equations, is developed to calculate precisely the acoustic eigenfrequencies and their associated eigenvectors, located in a given high frequency interval. It is currently known ...
Eigenvalues for systems of fractional p-Laplacians
(Rocky Mt Math Consortium, 2018-12)
We study the eigenvalue problem for a system of fractional p-Laplacians, that is, (-Δp)ru=λαp|u|α-2u|v|β(-Δp)sv=λβp|u|α|v|β-2vu=v=0in Ω,in Ω,in Ωc=RNΩ. We show that there is a first (smallest) eigenvalue that is simple and ...
The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians
(Springer Heidelberg, 2016-10)
In this paper, we study the behavior as p→ ∞ of eigenvalues and eigenfunctions of a system of p-Laplacians, that is (Formula presented.) in a bounded smooth domain Ω. Here α+ β= p. We assume that α/p→Γ and β/p→1-Γ as p→ ∞ ...