Interpolatory product quadratures for Cauchy principal value integrals with Freud weights

Citation
Sb. Damelin et K. Diethelm, Interpolatory product quadratures for Cauchy principal value integrals with Freud weights, NUMER MATH, 83(1), 1999, pp. 87-105
Citations number
15
Categorie Soggetti
Mathematics
Journal title
NUMERISCHE MATHEMATIK
ISSN journal
0029599X → ACNP
Volume
83
Issue
1
Year of publication
1999
Pages
87 - 105
Database
ISI
SICI code
0029-599X(199907)83:1<87:IPQFCP>2.0.ZU;2-W
Abstract
We prove convergence results and error estimates for interpolatory product quadrature formulas for Cauchy principal value integrals on the real line w ith Freud-type weight functions. The formulas are based on polynomial inter polation at the zeros of orthogonal polynomials associated with the weight function under consideration. As a by-product, we obtain new bounds for the derivative of the functions of the second kind for these weight functions.