Computing

, Volume 48, Issue 1, pp 97–107 | Cite as

Constrained smoothing of histograms by quadratic splines

  • J. W. Schmidt
Article

Abstract

For smoothing histograms under constraints like convexity or monotonicity, in this paper the functionalsK2 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.

AMS (MOS) Subject Classification

65D10 41A15 90C25 

Key words

FunctionalsK2 andK, constraints like convexity or monotonicity linear programs partially separable programs and dualization Fenchel conjugates 

Restringiertes Glätten von Histogrammen unter Verwendung von quadratischen Splines

Zusammenfassung

Zum Glätten von Histogrammen unter Nebendedingungen wie Konvexität oder Monotonie werden die ZielfunktionaleK2 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.

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • J. W. Schmidt
    • 1
  1. 1.Institut für Numerische MathematikTechnische Universität DresdenDresdenFederal Republic of Germany

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