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  • 1
    Electronic Resource
    Electronic Resource
    Relative error in floating-point multiplication (1985)
    Springer
    Computing 35 (1985), S. 127-139 
    Details
    ISSN: 1436-5057
    Keywords: 65G05 ; 65G10 ; Relative error ; computer arithmetic ; floating point multiplication ; normalization options ; guard digits ; floating point numbers ; floating point precision and significance ; round-off error ; fraction error ; mean and standard deviation of errors ; logarithmically distributed numbers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird ein Modell für den relativen Fehler bei der Gleitkomma-Multiplikation entwickelt unf für verschiedene Kombinationen der Arithmetikparameter stochastisch analysiert. Die Parameter sind die Basis, die Rundungsart, die Anzahl der Schutzstellen, und ob die Normalisierung vor oder nach dem Runden erfolgt. Bei einer angenommenen logarithmischen Verteilung für die Mantisse kommt man zu folgenden Schlüssen: 1. Der durchschnittliche relative Fehler bei der Multiplikation wächst mit der Basis. 2. Dieser Fehler wird minimal für die Basis 2 (am besten mit verborgenem ersten Bit) und recht groß für die Basis 16. 3. Die klassischen Schranken für den relativen Fehler sind pessimistisch. Ihre durchschnittliche Überschätzung wächst mit der Basis.
    Notes: Abstract A model of the relative error in floating point multiplication is developed and is analyzed stochastically for various choices of computer design parameters. These parameters include the base, the type of rounding rule, the number of guard digits, and whether the post-arithmetic normalization shift (if needed) is done before or after rounding. Under the assumption of logarithmic distribution for the fraction (mantissa), the major stochastic conclusions are: 1. The average relative error in multiplication increases as the base increases. 2. This error is minimized by selecting the machine base to be binary (better yet, binary with a hidden bit) and is rather large for machines with base 16. 3. The classical relative error bounds are pessimistic. The average overestimation by those bounds increases as the base increases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02260500
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  • 2
    Electronic Resource
    Electronic Resource
    Electrophoretic and serological comparisons of pathogenesis-related (b) proteins from different plant species (1983)
    Springer
    European journal of plant pathology 89 (1983), S. 293-303 
    Details
    ISSN: 1573-8469
    Keywords: Gynura aurantiaca ; Lycopersicon esculentum ; Malus sylvestris ; amphidiploïdNicotiana glutinosa x Nicotiana debneyi ; Nicotiana sylvestris ; Nicotiana tabacum ; Phaseolus vulgaris ; Vigna sinensis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Preparations of pathogenesis-related (b) proteins (PRs) from differentNicotiana species, tomato,Gynura aurantiaca, bean, and cowpea were compared to each other and to bean chitinase and a constitutive apple agglutinin by electrophoresis in polyacrylamide gels both in the absence and in the presence of SDS, and by serological double diffusion analysis using antisera against tobacco PRs and bean chitinase. PRs from different plant genera displayed a similar but not identical range of relative mobilities in both native and SDS gels, whereas bean chitinase and apple agglutinin were clearly different. None of the antisera reacted with any of the PR preparations from plant genera other than the one from which the antigen(s) had been derived. Whilst PRs within the genusNicotiana are serologically related and can be identical, PRs from different plant genera seem to be sufficiently different to be considered as genus-specific.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01995264
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    Paper (German National Licenses)
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