Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 475320, 12 pages
doi:10.1155/2009/475320
Research Article

The Average Errors for the Grünwald Interpolation in the Wiener Space

Yingfang Du1 and Huajie Zhao2

1College of Chemistry and Life Science, Tianjin Normal University, Tianjin 300387, China
2Department of Mathematics, Tianjin Normal University, Tianjin 300387, China

Received 15 May 2009; Accepted 10 June 2009

Academic Editor: Guang Zhang

Copyright © 2009 Yingfang Du and Huajie Zhao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. F. Traub, G. W. Wasilkowski, and H. Woźniakowski, Information-Based Complexity, Computer Science and Scientific Computing, Academic Press, Boston, Mass, USA, 1988. View at Zentralblatt MATH · View at MathSciNet
  2. K. Ritter, “Approximation and optimization on the Wiener space,” Journal of Complexity, vol. 6, no. 4, pp. 337–364, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. F. J. Hickernell and H. Woźniakowski, “Integration and approximation in arbitrary dimensions,” Advances in Computational Mathematics, vol. 12, no. 1, pp. 25–58, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. M. Kon and L. Plaskota, “Information-based nonlinear approximation: an average case setting,” Journal of Complexity, vol. 21, no. 2, pp. 211–229, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. G. Grünwald, “On the theory of interpolation,” Acta Mathematica, vol. 75, pp. 219–245, 1943. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. Y. S. Sun and C. Y. Wang, “Average error bounds of best approximation of continuous functions on the Wiener space,” Journal of Complexity, vol. 11, no. 1, pp. 74–104, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. K. Ritter, Average-Case Analysis of Numerical Problems, vol. 1733 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2000. View at MathSciNet
  8. A. K. Varma and J. Prasad, “An analogue of a problem of P. Erdös and E. Feldheim on Lp convergence of interpolatory processes,” Journal of Approximation Theory, vol. 56, no. 2, pp. 225–240, 1989. View at Publisher · View at Google Scholar · View at MathSciNet