On the extreme eigenvalues of certain matrices of non-standard inner products of Hermite polynomials
Date
2018
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
We study Hermite orthogonal polynomials and Gram matrices of their non-standard inner products. The weight function of the non-standard inner product is obtained from the Gauss probability density function by its horizontal shift by a real parameter. We are interested in the spectral properties of these matrices and some of their modifications. We show how the largest and smallest eigenvalues of the matrices depend on the parameter.
Description
Subject(s)
Hermite polynomials, shifted Hermite polynomials, Gram matrix, reciprocal spectra, stochastic Galerkin method
Citation
ISSN
0024-3795