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Approximation Auf Dem Kubischen Gitter by S. G. Michlin

Approximation Auf Dem Kubischen Gitter

by S. G. Michlin
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Book cover type: Paperback
  • ISBN13: 9783034855006
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Birkhauser
  • Publisher Imprint: Birkhauser
  • Publication Date:
  • Pages: 195
  • Original Price: EUR 51.39
  • Language: German
  • Edition: Softcover Repri
  • Item Weight: 341 grams
  • BISAC Subject(s): General

Die vorliegende kleine Monographie knüpft an zwei Gebiete der Analysis an. Das eine ist die Variationsdifferenzenmethode zur näherungsweisen Lösung von Randwertaufgaben für Differentialgleichungen; dafür ist auch der Name Me- thode der finiten Elemente gebräuchlich. Das andere Gebiet ist die Konstruktive Funktionentheorie. Unser Ausgangspunkt ist der Aufbau spezieller Klassen von Koordinatenfunktionen für die Variationsdifferenzenmethode durch elementare Transformationen der unabhängigen Variablen aus gewissen vorgegebenen Funktionen, die der Verfasser Ausgangsfunktionen nennt. Sind diese Koordina- tenfunktionen konstruiert, entsteht die Frage nach ihren Linearkombinationen, mit denen Funktionen der einen oder der anderen vorgegebenen Klasse approxi- miert werden können, sowie die Frage nach dem Genauigkeitsgrad einer solchen Approximation in dieser oder jenen Norm. Das ist bereits ein Problem der Kon- struktiven Funktionentheorie. Die Monographie besteht aus elf Kapiteln. Im ersten Kapitel wird die Idee von R. CoURANT erörtert, die die Grundlage der Variationsdifferenzenmethode bildet. Ausführlich wird ein Beispiel von CouRANT diskutiert, und anband des Beispiels wird der Begriff der Ausgangsfunktion eingeführt. Es wird die all- gemeine Definition dieses Begriffes gegeben und ein Verfahren zur Konstruk- tion von Koordinatenfunktionen aufgezeigt.

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