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  • 1
    Electronic Resource
    Electronic Resource
    On the number of best Approximations in certain non-linear families of functions (1975)
    Springer
    Aequationes mathematicae 12 (1975), S. 184-199 
    Details
    ISSN: 1420-8903
    Keywords: 41A50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Zusammenfassung Sieht man von der rationalen Approximation und einigen anderen bekannten Beispielen ab, so muß man bei der nichtlinearen Approximation durchweg mit mehreren Lösungen rechnen. In der vorliegenden Arbeit wird anhand von instruktiven Beispielen gezeigt, wie man die Anzahl der Lösungen abschätzen kann, wenn die lokale Haarsche Bedingung — aber nicht notwendig die globale Haarsche Bedingung — erfüllt ist. Die globale Analyse wird dabei durch eine „local strong unicity condition“ ermöglicht.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01836547
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  • 2
    Electronic Resource
    Electronic Resource
    On the degree of approximation by spline functions with free knots (1975)
    Springer
    Aequationes mathematicae 12 (1975), S. 80-81 
    Details
    ISSN: 1420-8903
    Keywords: 41A15 ; 41A50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A comparison theorem is derived for Chebyshev approximation by spline functions with free knots. This generalizes a result of Bernstein for approximation by polynomials.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01834039
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  • 3
    Electronic Resource
    Electronic Resource
    Rational approximation of Stieltjes functions by the Carathéodory-Fejér method (1987)
    Springer
    Constructive approximation 3 (1987), S. 43-50 
    Details
    ISSN: 1432-0940
    Keywords: Rational approximation ; Stieltjes functions ; Carathéodory-Fejér method ; 41A50 ; 41A20 ; 30E110
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The Carathéodory-Fejér method provides a way for the construction of near best rational approximations. Gutknecht and Trefethen [7], [10] observed that in many cases the constructed functions yield very good estimates of the degree of rational approximation. We will Show that the correct asymptotic is obtained when the method is applied to Stieltjes functions. This fact is of interest in connection with Magnus' considerations of the 1/9-conjecture [9].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01890552
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