Non-iterative computation of Gauss-Jacobi quadrature by asymptotic expansions for large degree Article Swipe

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Amparo Gil , Javier Segura , Nico Μ. Τemme ·

YOU? · · 2018 · Open Access · · OA: W2797475162

Asymptotic approximations to the zeros of Jacobi polynomials are given, with methods to obtain the coefficients in the expansions. These approximations can be used as standalone methods for the non-iterative computation of the nodes of Gauss--Jacobi quadratures of high degree (n≥100). We also provide asymptotic approximations for functions related to the first order derivative of Jacobi polynomials which can be used to compute the weights of the Gauss--Jacobi quadrature. The performance of the asymptotic approximations is illustrated with numerical examples.