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Effective Numerical Methods and Average Errors

  • Erich Novak
Conference paper

Abstract

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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References

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    E. Novak, Deterministic and stochastic error bounds in numerical analysis. Springer 1988, Lecture Notes in Mathematics 1349.Google Scholar
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    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
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    E. Novak, Quadrature formulas for monotone functions. Proc. of the AMS 115 (1992), 59–68.CrossRefGoogle Scholar
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    E.Novak, K. Ritter, Average errors for zero finding: lower bounds. Mathematische Zeitschrift, to appear.Google Scholar
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    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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