Abstract
AbstractWe construct bivariate orthogonal polynomials (OPs) on algebraic curves of the form in where and ϕ is a polynomial of arbitrary degree d, 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.
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