Orthogonal polynomials on a class of planar algebraic curves
Marco Fasondini, Sheehan Olver, Yuan Xu · Studies in Applied Mathematics · 2023
Abstract We construct bivariate orthogonal polynomials (OPs) on algebraic curves of the form in where and ϕ is a polynomial of arbitrary degreed, in terms of univariate semiclassical OPs. We compute connection coefficients that relate the bivariate OPs to a polynomial basis that is itself orthogonal and whose span contains the OPs as a subspace. The connection matrix is shown to be banded and the connection coefficients and Jacobi matrices for OPs of degree are computed via the Lanczos algorithm in operations.