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  • 1
    Electronic Resource
    Electronic Resource
    Unrestricted algorithms for reciprocals and square roots (1986)
    Springer
    BIT 26 (1986), S. 475-492 
    Details
    ISSN: 1572-9125
    Keywords: Primary 65D20 ; Computer arithmetic ; error analysis ; multiple-precision software ; relative precision ; unrestricted alborithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Algorithms are presented for the computation of reciprocals of nonzero real numbers and square roots of positive numbers. There are no restrictions on the range of the numbers or on the precision that may be demanded in the results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01935054
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Algorithms for Special Functions I (1962)
    Springer
    Numerische Mathematik 4 (1962), S. 403-419 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01386339
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Root squaring using level-index arithmetic (1989)
    Springer
    Computing 43 (1989), S. 171-185 
    Details
    ISSN: 1436-5057
    Keywords: 65G99 ; 65H05 ; Level-index ; symmetric level-index ; root-squaring ; polynomial equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Das “symmetrische Höhenindexsystem” (sli) zur Zahlendarstellung vereinfacht die Überwachung der Rechengenauigkeit und vermeidet overflow—oder underflow—Probleme. In dieser Arbeit werden die praktischen Vorzüge des Systems am Beispiel des Graeffeverfahrens vorgeführt.
    Notes: Abstract The symmetric level-index,sli, system for representing numbers eases the monitoring of precision while avoiding the problems associated with overflow and underflow. In this paper the practical benefits of the system are displayed, using the root-squaring method of Graeffe as a vehicle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02241860
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    A method for numerical integration on an automatic computer (1960)
    Springer
    Numerische Mathematik 2 (1960), S. 197-205 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new method for the numerical integration of a “well-behaved” function over a finite range of argument is described. It consists essentially of expanding the integrand in a series of Chebyshev polynomials, and integrating this series term by term. Illustrative examples are given, and the method is compared with the most commonly-used alternatives, namelySimpson's rule and the method ofGauss.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01386223
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    Paper (German National Licenses)
    Fulltext
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