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Numerische Methoden Der Approximation Und Semi-Infiniten Optimierung

Numerische Methoden Der Approximation Und Semi-Infiniten Optimierung

          
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About the Book

Zur Theorie der Chebyshev-Approximation stetiger Funktionen gibt es eine Reihe ausgezeichneter Lehrbücher. Behandelt werden dort vor allem Probleme, die in Verallgemeinerung des klassischen Pro- blems der Approximation durch Polynome eine spezielle Vorausset- zung - die sog. Haar-Bedingung - in irgendeiner Form erfüllen, was eine ganze Reihe angenehmer Konsequenzen hat hinsichtlich der Cha- rakterisierung und der Eindeutigkeit der Lösungen. Dies setzt sich fort in den numerischen Verfahren zur Berechnung bester Approxima- tionen, die, wie etwa die bekannten Remes-Verfahren, auf diese speziellen Probleme zugeschnitten sind und bei nicht erfüllter Haar-Bedingung entweder völlig versagen oder nicht mehr effizient sind. Auf der anderen Seite führt eine ganze Reihe wichtiger An- wendungen auf Probleme, die für die Haar-Bedingung nicht erfüllt ist; sei es, daß Funktionen in mehreren Variablen zu approximieren sind, was die Haar-Bedingung grundsätzlich ausschließt, oder daß man wie bei der Behandlung gewisser Randwertprobleme in der Wahl der Ansatzfunktionen nicht frei ist, oder daß die approximierenden Funktionen noch zusätzliche Nebenbedingungen erfüllen sollen. Das hauptsächliche Anliegen dieses Buches ist es, diese Lücke zu schließen und eine Palette derzeit verfügbarer Methoden darzustel- len, die unter praxisnäheren Voraussetzungen arbeiten. Hierzu bie- tet es sich an, das Approximationsproblem als Optimierungsaufgabe zu formulieren und zu behandeln, da einerseits bei Wegfall der Haar-Bedingung das Chebyshev-Approximationsproblem kaum mehr Struktur als allgemeine Optimierungsprobleme aufweist, und ander- erseits auf diese Art die weit entwickelten, leistungsfähigen Me- thoden der Optimierung für die Approximation nutzbar werden.


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Product Details
  • ISBN-13: 9783519020639
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Height: 216 mm
  • No of Pages: 233
  • Series Title: Teubner Studienbücher Mechanik
  • Weight: 277 gr
  • ISBN-10: 3519020637
  • Publisher Date: 01 Mar 1982
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Spine Width: 13 mm
  • Width: 140 mm


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