References

AF: JuliaApproximation. ApproxFun.jl. https://github.com/JuliaApproximation/ApproxFun.jl.
ATAP: L. N. Trefethen. Approximation Theory and Approximation Practice, extended edition. SIAM, Philadelphia, 2019.
Bar75: S. Barnett. A companion matrix analogue for orthogonal polynomials. Linear Algebra and its Applications, 12(3):197–208, 1975.
Cle55: C. W. Clenshaw. A note on the summation of Chebyshev series. Mathematical Tables and Other Aids to Computation, 9(51):118–120, 1955.
DHT14: T. A. Driscoll, N. Hale, and L. N. Trefethen, editors. Chebfun Guide. Pafnuty Publications, Oxford, 2014. https://www.chebfun.org/docs/guide/.
DLMF: F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V. Saunders, H. S. Cohl, and M. A. McClain, editors. NIST Digital Library of Mathematical Functions. https://dlmf.nist.gov/.
DX14: C. F. Dunkl and Y. Xu. Orthogonal Polynomials of Several Variables, 2nd edition. Encyclopedia of Mathematics and its Applications 155. Cambridge University Press, 2014.
Gau70: W. Gautschi. On the construction of Gaussian quadrature rules from modified moments. Mathematics of Computation, 24:245–260, 1970.
GCO22: T. S. Gutleb, J. A. Carrillo, and S. Olver. Computing equilibrium measures with power law kernels. Mathematics of Computation, 91, 2022. arXiv:2011.00045.
Goo61: I. J. Good. The colleague matrix, a Chebyshev analogue of the companion matrix. The Quarterly Journal of Mathematics, 12(1):61–68, 1961.
GO20: T. S. Gutleb and S. Olver. A sparse spectral method for Volterra integral equations using orthogonal polynomials on the triangle. SIAM Journal on Numerical Analysis, 58(3), 2020. arXiv:1906.03907.
GOS25: T. S. Gutleb, S. Olver, and R. M. Slevinsky. Polynomial and rational measure modifications of orthogonal polynomials via infinite-dimensional banded matrix factorizations. Foundations of Computational Mathematics, 25(5):1463–1505, 2025. arXiv:2302.08448.
Gut22: T. S. Gutleb. Sparse spectral methods for integral equations and equilibrium measures. PhD thesis, Imperial College London, 2022. doi:10.25560/100138.
GVL13: G. H. Golub and C. F. Van Loan. Matrix Computations, 4th edition. Johns Hopkins University Press, 2013.
GW69: G. H. Golub and J. H. Welsch. Calculation of Gauss quadrature rules. Mathematics of Computation, 23:221–230, 1969.
MOP: JuliaApproximation. MultivariateOrthogonalPolynomials.jl. https://github.com/JuliaApproximation/MultivariateOrthogonalPolynomials.jl.
OT13: S. Olver and A. Townsend. A fast and well-conditioned spectral method. SIAM Review, 55(3):462–489, 2013. doi:10.1137/120865458, arXiv:1202.1347.
OT14: S. Olver and A. Townsend. A practical framework for infinite-dimensional linear algebra. In Proceedings of the First Workshop for High Performance Technical Computing in Dynamic Languages, pages 57–62, 2014. doi:10.1109/HPTCDL.2014.10.
PGSO24: I. P. A. Papadopoulos, T. S. Gutleb, R. M. Slevinsky, and S. Olver. Building hierarchies of semiclassical Jacobi polynomials for spectral methods in annuli. SIAM Journal on Scientific Computing, 46(6):A3448–A3476, 2024. arXiv:2310.07541.
Sze75: G. Szegő. Orthogonal Polynomials, 4th edition. American Mathematical Society Colloquium Publications 23. AMS, Providence, RI, 1975.
Tre08: L. N. Trefethen. Is Gauss quadrature better than Clenshaw–Curtis? SIAM Review, 50(1):67–87, 2008.
Lin85: P. Linz. Analytical and Numerical Methods for Volterra Equations. SIAM, Philadelphia, 1985. https://doi.org/10.1137/1.9781611970852.