Skip Navigation



IMA Journal of Numerical Analysis Advance Access published online on May 16, 2008
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drm040
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Milovanovic, G. V.
Right arrow Articles by Pranic, M. S.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Error estimates for Gauss–Turán quadratures and their Kronrod extensions

Gradimir V. Milovanovic

Faculty of Electronic Engineering, Department of Mathematics, University of Nis, PO Box 73, 18000 Nis, Serbia

Miodrag M. Spalevic{dagger}

Faculty of Science, Department of Mathematics and Informatics, University of Kragujevac, PO Box 60, 34000 Kragujevac, Serbia

Miroslav S. Pranic

Faculty of Science, Department of Mathematics and Informatics, University of Banja Luka, M. Stojanovi a 2, 51000 Banja Luka, Bosnia and Herzegovina

{dagger} Email: spale{at}kg.ac.yu

Received on 18 March 2007. Revised on 29 October 2007.


  Abstract

We study the kernel Kn, s(z) of the remainder term Rn, s(f) of Gauss–Turán–Kronrod quadrature rules with respect to one of the generalized Chebyshev weight functions for analytic functions. The location on the elliptic contours where the modulus of the kernel attains its maximum value is investigated. This leads to effective L{infty}-error bounds of Gauss–Turán–Kronrod quadratures. Following Kronrod, using the modulus of the difference of Gauss–Turán quadratures and their Kronrod extensions, we derive new error estimates for Gauss–Turán quadratures and compare them with the effective L1-error bounds derived in Milovanovic & Spalevic (2005, BIT, 45, 117–136).

Key Words: Gauss–Turán quadratures; Kronrod extensions; s-orthogonal polynomials; Stieltjes polynomials; remainder term; error estimate; analytic function


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.