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  • 1
    Electronic Resource
    Electronic Resource
    Comments on a root finding method using Padé approximation (1977)
    Springer
    BIT 17 (1977), S. 360-361 
    Details
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this note the results of A. Nourein [8] are related to the existing literature, and a more efficient computational procedure than the one given therein is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01932157
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A new technique for rational extrapolation to the limit (1971)
    Springer
    Numerische Mathematik 17 (1971), S. 215-221 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Zusammenfassung Es werden zwei neue Extrapolationsverfahren angegeben. Die beiden Verfahren sind entwickelt aus dem Gebrauch von Kettenbrüchen als interpolierende Funktionen und unendlich als Extrapolationspunkt. Einige Beziehungen mit dem Algorithmus von Bulirsch und Stoer (zur rationalen Extrapolation) und dem ε-Algorithmus (zur Bestimmung des Limes einer Folge) werden gezeigt. Einige Beispiele illustrieren den Gebrauch dieser Verfahren und ihre Konvergenz.
    Notes: Summary Two new algorithms are proposed for extrapolation to the limit. Both algorithms are based on the use of continued fractions as interpolating functions and infinity as extrapolation point. Some relationships with the algorithm, of Bulirsch and Stoer (for rational extrapolation) and the ε-algorithm (for defining the limit of a sequence) are given. Some examples illustrate the usefulness of the given algorithms and their convergence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01436377
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Characterization of minimal elements in minimization problems with constraints (1978)
    Springer
    Journal of optimization theory and applications 24 (1978), S. 549-567 
    Details
    ISSN: 1573-2878
    Keywords: Minimization with constraints ; generalized weight function ; characterization theorems ; critical point ; extremal signature
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetX be a compact Hausdorff space andC(X) be the set of all continuous functions defined onX. LetV⊂C(X), and consider the problem of minimizing sup x∈X W[x,v(x)], withv∈V. The functionW is a generalized weight function and can be chosen such that certain constraints are included. The notions of critical point and extremal signature are used to formulate characterization theorems for a minimal element inV. It is shown that these theorems hold only under certain conditions ofV andW. The results obtained are applied to the problem of the Chebyshev approximation with constraints and to the problem of optimization with strictly quasiconvex constraints.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935299
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    Paper (German National Licenses)
    Fulltext
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