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Vorlesung Über Approximationstheorie by Helmut Werner

Vorlesung Über Approximationstheorie

by Helmut Werner
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Book cover type: Paperback
  • ISBN13: 9783540035978
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 196
  • Original Price: EUR 26.16
  • Language: German
  • Edition: 1966
  • Item Weight: 291 grams
  • BISAC Subject(s): Algebra / General

Dieses Manuskript ist die Ausarbeitung einer im Sommersemester 1964 gehaltenen Vorlesung deren Ziel es war, die Horer mit den Problemen der Approximationstheorie vertraut zu machen, die die Grundlage des numerischen Arbeitens bilden. Da keine speziellen Vorkenntnisse vorausgesetzt wurden mu ten auch die klassischen Fragen behandelt oder enigstens gestreift werden. Den Hauptgegenstand bildete die Theorie der Tschebyscheff-Approximation stetiger Funktionen. Im Gegensatz zu der EinfUhrung von J. Rice (siehe Literatur-Ver- zeichnis [1964J ) wurden Polynom-Approximation und rationale Approximation gemeinsam behandelt, da man vielraeh die gleiehen qUalitativen Resultate erhalt, wenn man'normal Funktionen verwendet. Leider trifft diese Feststellung fUr die Konvergenz des Remes-Algo- rithmus im Gro5en nicht zu. Obgleieh seit Niedersehri t der Vorle- sung weitere Ergebnisse erzielt worden sind, steht eine vollige Klarung der Verhaltnisse noeh aus. Siehere Algorithmen zur Bereehnung der rationalen Tsehebyseheff-Approximierenden sind sebr schwerfallig, andere, die elegant sind, konvergieren nur, wenn die Ansatzfunktion bereits gut genug war. Der als Anhang beigefligte Algorithmus stellt einen, hoffentlieh guten, KompromiS dar. Folgerungen aus Eigensehaften der zu approximierenden Funktion, die fiber die Stetigkeit hinausgehen, konnten aus Zeitmangel kaum berueksichtigt werden. Es kann in dieser Hinsieht auf das Bueh von G. Meinardus [1964J verwiesen werden. Ieh danke Herrn Dipl.-Math. G. Lamprecht fur die Anfertigung der Vorlesungsnachschrift, den Herren Dipl.-Hath. H. Biermann und Dipl.-l-1ath. W. Dost sowie Frau Stud.Assessorin I. Werner fiir die Hilfe bei der Korrektur.

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