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- W2951902738 abstract "The computation of the entries of Jacobi operators associated with orthogonal polynomials has important applications in numerical analysis. From truncating the operator to form a Jacobi matrix, one can apply the Golub--Welsh algorithm to compute the Gaussian quadrature weights and nodes. Furthermore, the entries of the Jacobi operator are the coefficients in the three-term recurrence relationship for the polynomials. This provides an efficient method for evaluating the orthogonal polynomials. Here, we present an $mathcal O(N)$ method to compute the first $N$ rows of Jacobi operators from the associated weight. The method exploits the Riemann--Hilbert representation of the polynomials by solving a deformed Riemann--Hilbert problem numerically. We further adapt this computational approach to certain entire weights that are beyond the reach of current asymptotic Riemann--Hilbert techniques." @default.
- W2951902738 created "2019-06-27" @default.
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- W2951902738 date "2013-11-22" @default.
- W2951902738 modified "2023-09-27" @default.
- W2951902738 title "A Riemann--Hilbert approach to Jacobi operators and Gaussian quadrature" @default.
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