Effective Numerical Methods and Average Errors

  • Erich Novak
Conference paper


The final aim of numerical analysis is the construction and identification of effective numerical methods. Generally spoken, an effective method should be stable in a certain sense and also its error should be small compared to its computational cost. We do not discuss stability here and of course we do not have a definition of an ‘effective method’ that could always be applied. We only have several notions of the error and the cost of a method on one side and some heuristic ideas acquired by many numerical calculations on the other side.


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  1. 1.
    E. Novak, Deterministic and stochastic error bounds in numerical analysis. Springer 1988, Lecture Notes in Mathematics 1349.Google Scholar
  2. 2.
    E. Novak, Algorithms and complexity for continuous problems. To appear in: Geometry, Analysis, and Mechanics, J. M. Rassias (ed.), World Scientific Publishing, Singapore, 1992.Google Scholar
  3. 3.
    E. Novak, Quadrature formulas for monotone functions. Proc. of the AMS 115 (1992), 59–68.CrossRefGoogle Scholar
  4. 4.
    E.Novak, K. Ritter, Average errors for zero finding: lower bounds. Mathematische Zeitschrift, to appear.Google Scholar
  5. 5.
    J. F. Traub, G. W. Wasilkowski, H. Woźniakowski, Information-based complexity. Academic Press 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Erich Novak
    • 1
  1. 1.Mathematisches InstitutUniversität ErlangenErlangenGermany

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