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Optimierung Und Approximation by Werner Krabs

Optimierung Und Approximation

by Werner Krabs
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Book cover type: Paperback
  • ISBN13: 9783519020554
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Publication Date:
  • Pages: 209
  • Original Price: EUR 46.68
  • Language: German
  • Edition: 1975
  • Item Weight: 250 grams
  • BISAC Subject(s): Engineering (General)

Dieses Buch ist dem lusammenhang zwischen Optimierung und Approximation gewid- met. Es ist aus Vorlesungen hervorgegangen, die ich in den Jahren 1971 bis 1973 in Aachen und Darmstadt gehalten habe. Die Approximationstheorie hat sich zunachst als selbstandige Disziplin entwickelt, und auch der Optimierungstheorie lagen zu Beginn andere lielsetzungen als die Anwendung auf Approximationsprobleme zugrunde. Eine so1che Anwendung liegt aber sehr nahe, da man jedes Approximationsproblem auch als eine Optimierungsaufgabe auffassen kann. Bei der SUbsumption der Approximation unter das allgemeinere Konzept der Optimierung gehen zweifellos speziellere Eigenschaften des Approximationsproblerns verloren, so daB man nicht hoffen kann, alle approximationstheoretischen Fragen auf dem Wege tiber die Optimierung zu beantworten. Bei der Frage nach der Charakterisierung bester Approximierender und nach der Berech- nung oder Abschatzung der Minimalabweichung hat sich jedoch der Einsatz der Opti- mierungstheorie als sehr fruchtbar erwiesen. Auch bei der Frage nach der Existenz bester Approximierender liefert sie wertvolle Anhaltspunkte, weniger jedoch bei der Eindeu- tigkeit, die in der Optimierung eine untergeordnete Rolle spielt. Nicht zuletzt lassen sich auch die mannigfachen Methoden zur Uisung von Optimierungsproblemen mit Gewinn auf Approximationsaufgaben anwenden, worauf allerdings in diesem Buch nicht einge- gangen wird. Seine lielsetzung besteht vie1mehr darin zu zeigen, wie sich zahlreiche verschiedenartige Approximationsprobleme, die sich zum Teil aus direkten physikalisch-technischen Anwendungen und zum Teil aus anderen Fragestellungen der angewandten Mathematik ergeben, im Rahmen der Optimierungstheorie einheitlich behandeln lassen.

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