Numerische Mathematik

, Volume 84, Issue 3, pp 497–518

Estimating quadrature errors for analytic functions using kernel representations and biorthogonal systems

Authors

  • Rudolf Scherer
    • Institut für Praktische Mathematik der Universität Karlsruhe, D-76128 Karlsruhe, Germany; e-mail: scherer@math.uni-karlsruhe.de
  • Thomas Schira
    • Institut für Praktische Mathematik der Universität Karlsruhe, D-76128 Karlsruhe, Germany; e-mail: scherer@math.uni-karlsruhe.de
Original article

DOI: 10.1007/s002110050007

Cite this article as:
Scherer, R. & Schira, T. Numer. Math. (2000) 84: 497. doi:10.1007/s002110050007

Summary. For analytic functions the remainder term of quadrature rules can be represented as a contour integral with a complex kernel function. From this representation different remainder term estimates involving the kernel are obtained. It is studied in detail how polynomial biorthogonal systems can be applied to derive sharp bounds for the kernel function. It is shown that these bounds are practical to use and can easily be computed. Finally, various numerical examples are presented.

Mathematics Subject Classification (1991):41A55; 65D30, 65D32
Download to read the full article text

Copyright information

© Springer-Verlag Berlin Heidelberg 2000