authors
- CALLE YSERN, BERNARDO DE LA
- LOPEZ LAGOMASINO, GUILLERMO
- REICHEL ., LOTHAR
Stieltjes-type Polynomials on the Unit Circle
Articles
Overview
published in
- MATHEMATICS OF COMPUTATION Journal
publication date
- June 2009
start page
- 969
end page
- 997
issue
- 266
volume
- 78
Digital Object Identifier (DOI)
International Standard Serial Number (ISSN)
- 0025-5718
Electronic International Standard Serial Number (EISSN)
- 1088-6842
abstract
- Stieltjes-type polynomials corresponding to measures supported on the unit circle T are introduced and their asymptotic properties away from T are studied for general classes of measures. As an application, we prove the convergence of an associated sequence of interpolating rational functions to the corresponding Carathéodory function. In turn, this is used to give an estimate of the rate of convergence of certain quadrature formulae that resemble the Gauss-Kronrod rule, provided that the integrand is analytic in a neighborhood of T.