A Riemann–Hilbert approach to Jacobi operators and Gaussian quadrature

@inproceedings{Trogdon2013ARA,
  title={A Riemann–Hilbert approach to Jacobi operators and Gaussian quadrature},
  author={Thomas Trogdon},
  year={2013}
}
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… CONTINUE READING