In this paper, the authors give a different and more precise analysis of the stability of the classical Gauss-Laguerre quadrature rule for the
Cauchy P.V. integrals on the half line. Moreover, in order to obtain this
result they give some new estimates for the distance of the zeros of the
Laguerre polynomials that can be useful also in other contests.
References
[1]
Shen, W. (2019) An Introduction to Numerical Computation World Scientific. World Scientific Publishing Company. https://doi.org/10.1142/11388
[2]
Capobianco, M.R., Criscuolo, G. and Giova, R. (2001) A Stable and Convergent Algorithm to Evaluate Hilbert Transform. Numerical Algorithms, 28, 11-26. https://doi.org/10.1023/A:1014009809919
[3]
Ditzian, Z. and Lubinsky, D.S. (1997) Jackson and Smoothness Theorems for Freud Weights. Constructive Approximation, 13, 99-152. https://doi.org/10.1007/BF02678431
[4]
Freud, G. (1971) Orthogonal Polynomials. Pergamon Press, Budapest.
[5]
Szegö, G. (1975) Orthogonal Polynomials. American Mathematical Society, Providence, Rhode Island.
[6]
Levin, E. and Lubinsky, D.S. (2005) Orthogonal Polynomials for Exponential Weights x2pe-2Q(x) on . Journal of Approximation Theory, 134, 199-256. https://doi.org/10.1016/j.jat.2005.02.006
[7]
Levin, E. and Lubinsky, D.S. (2006) Orthogonal Polynomials for Exponential Weights x2pe-2Q(x) on , II. Journal of Approximation Theory, 139, 107-143. https://doi.org/10.1016/j.jat.2005.05.010
