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  • 65D10  (2)
  • Springer  (2)
  • American Association for the Advancement of Science
  • American Chemical Society
  • Springer Nature
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  • Springer  (2)
  • American Association for the Advancement of Science
  • American Chemical Society
  • Springer Nature
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  • 1
    Electronic Resource
    Electronic Resource
    Constrained smoothing of histograms by quadratic splines (1992)
    Springer
    Computing 48 (1992), S. 97-107 
    Details
    ISSN: 1436-5057
    Keywords: 65D10 ; 41A15 ; 90C25 ; FunctionalsK 2 andK ∞, constraints like convexity or monotonicity ; linear programs ; partially separable programs and dualization ; Fenchel conjugates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Zum Glätten von Histogrammen unter Nebendedingungen wie Konvexität oder Monotonie werden die ZielfunktionaleK 2 undK ∞ vorgeschlagen, welche dem bekannten Schoenberg-Funktional von der Datenglättung nachgebildet sind. Bei Verwendung von quadratischen Splines erhält man strukturierte, endlichdimensionale Optimierungsaufgaben. Auftretende partiell separable, konvexe Aufgaben können durch Dualisierung einer effektiven numerischen Behandlung zugeführt werden.
    Notes: Abstract For smoothing histograms under constraints like convexity or monotonicity, in this paper the functionalsK 2 andK ∞ are proposed which can be considered as extensions of the Schoenberg functional known from data smoothing. When using quadratic splines we are led to structured finite dimensional programming problems. Occuring partially separable convex programs can be solved effectively via dualization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02241708
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  • 2
    Electronic Resource
    Electronic Resource
    An unconstrained dual program for computing convexC 1-spline approximants (1987)
    Springer
    Computing 39 (1987), S. 133-140 
    Details
    ISSN: 1436-5057
    Keywords: 65D10 ; 41A15 ; 90C20 ; Specially structured optimization problem ; Fenchel dualization ; return-formula
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird die Aufgabe betrachtet, eine vorgegebene Datenmenge durch konvexe kubischeC 1-Splines zu approximieren. Zu diesem Problem wird eine zugehörige duale Optimierungsaufgabe konstruiert, welche den Vorteil hat, daß keine Nebenbedingungen auftreten, und welche sich daher effektiver als das Ausgangsproblem numerisch behandeln läßt.
    Notes: Abstract In the present paper the problem of approximating given data sets by convex cubicC 1-splines is considered. To this programming problem a dual program is constructed which is unconstrained. Therefore an efficient computational treatment is possible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02310102
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    Paper (German National Licenses)
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