New Application Related Developments in Informatics with Verified Results

  • F. Krückeberg
Conference paper


For several scientific and technical applications we need computed results that can be automatically verified during the computing time. New Developments in Computer Science are Computer Algebra Systems and Highly Accurate Arithmetics with special Rounding Operations including Rounding Errors. The combining of Computer Algebra and Accurate Arithmetics with variable word length leads to a new class of hybrid methods producing verified results. The main ideas of these hybrid methods are explained and some examples are shown.


Hybrid Method Word Length Computer Algebra Double Precision Computer Algebra System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Jenks and others Scratchpad II: An Abstract Datatype System for Mathematical Computation, Mathematical Aspects of Scientific Software, Springer New York (1989)Google Scholar
  2. [2]
    Krückeberg Arbitrary Accuracy with Variable Precision Arithmetic. In: Interval Mathematics 1985, Lecture Notes in Computer Science 212, Hrsg.: K. Nickel, Springer Verlag 1985.Google Scholar
  3. [3]
    Lehmann Die Analytische Maschine. Grundlagen einer Computer-Analytik. Sitzungsberichte der Sächsischen Akademie der Wissenschaften zu Leipzig. Band 118, Heft 4 (1985).Google Scholar
  4. [4]
    Leisen Zur Erzielung variabel vorgebbarer Fehlereinschließungen für gewöhnliche Differentialgleichungen mit Anfangswertmengen mittels dynamisch steuerbarer Arithmetik. Diplomarbeit Universität Bonn, 1985Google Scholar
  5. [5]
    Schwarz Symmetries of Differential equations from Sophus Lie to Computer Algebra, SIAM Review, 30 (1988)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • F. Krückeberg
    • 1
  1. 1.Gesellschaft für Mathematik und DatenverarbeitungGermany

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