Generalized characteristic polynomials and Gaussian cubature rules
Classical Analysis and ODEs
2015-06-26 v2
Abstract
For a family of near banded Toeplitz matrices, generalized characteristic polynomials are shown to be orthogonal polynomials of two variables, which include the Chebyshev polynomials of the second kind on the deltoid as a special case. These orthogonal polynomials possess maximal number of real common zeros, which generate a family of Gaussian cubature rules in two variables.
Cite
@article{arxiv.1406.3329,
title = {Generalized characteristic polynomials and Gaussian cubature rules},
author = {Yuan Xu},
journal= {arXiv preprint arXiv:1406.3329},
year = {2015}
}