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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 57 (1990), S. 139-145 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D32 ; CR: G1.4
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Applying numerical quadrature to singular integrals in a straightforward way leads to uncontrolled instability with respect to data errors. In this paper we describe how to control this instability.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Trends in Biotechnology 11 (1993), S. 74-77 
    ISSN: 0167-7799
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 14 (1970), S. 246-251 
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 14 (1969), S. 14-23 
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 19 (1972), S. 49-55 
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary It is shown that the remainder term of any quadrature formula has an asymptotic expansion in terms of the step size; the occurrence of remainder terms of formc f (n+1) (ξ) is discussed.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Diabetologia 43 (2000), S. 1282-1292 
    ISSN: 1432-0428
    Keywords: Keywords Standards, ICA, GAD65, IA-2, diabetes, diagnostics, autoantibodies, islet cells.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Aims/hypothesis. Islet cell autoantibodies are a specific marker for Type 1 (insulin-dependent) diabetes mellitus. Standardisation of islet cell antibodies and the uniform reporting in International units is critical to research and the development of assays for islet cell autoantibodies as diagnostics.¶Methods. The suitability of a candidate serum to serve as the international standard for islet cell antibodies was studied by 19 participants in 8 countries. In addition, the purpose was to investigate whether the serum could also serve as a standard for antibodies to the 65 000 Mr isoform of glutamic acid decarboxylase (GAD65) and islet antigen-2 (IA-2). Control sera were included in the study to assess the validity of the various assay systems. The sera were lyophilized to World Health Organization criteria and the candidate serum assigned the ampoule code number 97/550.¶Results. The use of 97/550 was shown to notably reduce inter laboratory variability in the measurement of islet cell antibodies. In addition, there was a pronounced reduction in inter laboratory variability in the measurement of GAD65 and IA-2 antibodies. ¶Conclusions/interpretation. On the basis of the results reported here and with agreement of the participants, the preparation 97/550 has been established by the World Health Organization Expert Committee on Biological Standards for establishment as the first international standard for islet cell antibodies, with an assigned potency of 20 international units. In addition, 97/550 can serve as an international reference reagent for specific GAD65 antibodies, with an assigned potency of 100 units. It can also serve as a National Institute of Biological Standards and Control (NIBSC) reference reagent for IA-2 antibodies for evaluation of assays for this material. [Diabetologia (2000) 43: 1282–1292]
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 15 (1970), S. 74-86 
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 23 (1974), S. 241-254 
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In 1966 Golub and Wilkinson gave upper bounds for the errors of least squares solutions based on orthogonal transformations, in which the square of the condition number of the matrix occurs. In the present paper a geometrical explanation and lower bounds are given. The upper bounds will be shown to be realistic for some classes of problems and types of perturbations, and to be unrealistic for others.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 26 (1976), S. 61-78 
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A rigorous error analysis is given of both truncation and rounding errors in Miller's algorithm for three-term scalar recursions and 2×2 matrix-vector recursions. The error bounds are shown to be very realistic and this will be supported by examples. The results are generalized to recursions of higher order.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 48 (1986), S. 543-560 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65F10 ; CR: G.1.3
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary It has been observed that the rate of convergence of Conjugate Gradients increases when one or more of the extreme Ritz values have sufficiently converged to the corresponding eigenvalues (the “superlinear convergence” of CG). In this paper this will be proved and made quantitative. It will be shown that a very modest degree of convergence of an extreme Ritz value already suffices for an increased rate of convergence to occur.
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