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Über Alternationskriterien in der Geschichte der Besten Chebyshev-Approximation

Über Alternationskriterien in der Geschichte der Besten Chebyshev-Approximation

          
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About the Book

Diplomarbeit aus dem Jahr 1994 im Fachbereich Mathematik - Analysis, Note: 1,3, Johann Wolfgang Goethe-Universität Frankfurt am Main (Fachbereich Mathematik), Sprache: Deutsch, Abstract: Wenn wir uns die Aufgabe stellen, ein Bogenstück durch ein Geradenstück so anzunähern, dass der unterschied zwischen beiden Linien möglichst klein wird, so werden wir die Gerade immer so zu legen versuchen, dass sowohl rechts als auch links von ihr die maximale Abweichung gleich wird. Beispielsweise käme niemand auf die Edee, den Halbkreis durch eine Linie anzunähern, die genau dem Durchmesser entlangläuft. Vielmehr wird man hier die Gerade in die Mitte zu legen versuchen. Genau diese Idee verwendet Euler, um eine möglichst genaue Karte des russischen Reiches zu zeichnen: Er nähert die Erdkugel so durch eine Ebene an, dass der Fehler am nördlichsten Punkt, am südlichsten Punkt und "irgendwo in der Mitte" gleich ist. Nun könnte man vermuten, dass sie beste Näherung hier von der Lage dieses Punktes abhängt, jedoch nach dem Alternantensatz hängt vielmehr der Punkt von der Größe des minimale maximalen Fehlers ab, bzw. beide Werte korrespondieren miteinander. Der Satz, von dem in dieser Arbeit die Rede sein wird, verallgemeinert dieses im Falle von Gerade und Bogen noch sehr anschauliche Problem auf reelwertige stetige Funktionen, die durch Polynome, bzw. im noch allgemerineren Fall, auf Funktionen, die der Haar'schen Bedingung genügen, angenähert werden.


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Product Details
  • ISBN-13: 9783640860296
  • Publisher: Grin Publishing
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Spine Width: 7 mm
  • Width: 148 mm
  • ISBN-10: 3640860292
  • Publisher Date: 23 Mar 2011
  • Height: 210 mm
  • No of Pages: 120
  • Series Title: German
  • Weight: 168 gr


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