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  • 11
    Electronic Resource
    Electronic Resource
    Ratioanl biquadraicC 1-splines inS-convex interpolation (1991)
    Springer
    Computing 47 (1991), S. 87-96 
    Details
    ISSN: 1436-5057
    Keywords: 65D07 ; 41A15 ; 41A63 ; S-convex spline interpolation ; existence conditions ; search procedure for constructingS-convex splines
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbiet wird eine notwendige und hinreichende Bedingung für dieS-Konvexität von rational-biquadratischen Spline interpolierenden auf Rechteckgittern hergeleitet. Da Kriterium kann in Form von linearen Gleichungen und konvexen Ungleichungen formuliert werden, und es wird gezeigt, daß diese im Fall von hinreichend großen Rationalitätsparametern erfüllbar sind, sofer sind die zu interpolierende Datenmenge inS-konvexer Lage befindet.
    Notes: Abstract The purpose of this paper is to give a necessary and sufficient condition for theS-convexity of rational biquadraticC 1-spline interpolants on rectangular grids. The criterion is described in form of linear equalities and convex inequalities, and forS-convex data sets the criterion can be satisfied whenever the rationality parameters are sufficiently large.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02242024
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  • 12
    Electronic Resource
    Electronic Resource
    On the R-order of coupled sequences III (1983)
    Springer
    Computing 30 (1983), S. 157-169 
    Details
    ISSN: 1436-5057
    Keywords: 65H10 ; 15A48 ; Iterative parallel processes ; best individualR-orders ; ordered positive decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Für konvergente Folgen {x n,1 },...,{x n,s }, welche über ein System (2) von Ungleichungen miteinander verkoppelt sind, werden die besten individuellenR-Ordnungen τ1,...,τ s bestimmt. Dazu wird gezeigt, daß diese gleich den Spektralradien von bestimmten Matrizen sind, welche aus Exponenten in (2) gebildet werden.
    Notes: Abstract For convergent sequences {x n,1 },...{x n,s } coupled by a system (2) of inequalities the optimal individualR-orders τ1,...,τ s are determined as the spectral radii of certain matrices composed of exponents appearing in (2).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02280786
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    Paper (German National Licenses)
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  • 13
    Electronic Resource
    Electronic Resource
    Determination of the cone radius for positive concave operators (1984)
    Springer
    Computing 33 (1984), S. 37-49 
    Details
    ISSN: 1436-5057
    Keywords: 65H10 ; 90C30 ; 15A48 ; Iterative processes ; bestR-orders ; cone radius of concave operators ; spectral radii ; partial ordering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Berechnung der bestenR-Ordnung von Folgen aus iterativen Näherungsverfahren führt auf die Ermittlung des hier eingeführten Kegelradius bestimmter konkaver Operatoren. Das Hauptergebnis der Arbeit ist die Darstellung des Kegelradius als Infimum der Spektralradien aller den konkaven Operator majorisierenden linearen Operatoren. Diese Charakterisierung ist von numerischem Intersse.
    Notes: Abstract The computation of bestR-orders of sequences produced by iterative methods leads to the determination of the cone radius of certain concave operators. The main result of the paper is the representation of the cone radius as the infimum of spectral radii of all linear operators majorizing the concave operator. This characterization is of numerical interest.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02243074
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    Paper (German National Licenses)
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