Unmasking the Witchy Behavior of the Runge Function

Autor/inn/en	Cupillari, Antonella; DeThomas, Elizabeth
Titel	Unmasking the Witchy Behavior of the Runge Function
Quelle	In: Mathematics and Computer Education, 41 (2007) 2, S.143-156 (14 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0730-8639
Schlagwörter	Undergraduate Students; Textbooks; Intervals; Exhibits; Mathematics; Mathematics Education; Mathematical Logic; Validity; Mathematical Formulas; Graphs; Algebra; Logical Thinking; College Mathematics + Suchen Sie Ihr Suchwort? Textbook; Text book; Schulbuch; Lehrbuch; Mathematik; Mathematische Bildung; Mathematical logics; Mathematische Logik; Gültigkeit; Mathematische Formel; Grafische Darstellung
Abstract	It is in the field of numerical analysis that this "easy-looking" function, also known as the Runge function, exhibits a behavior so idiosyncratic that it is mentioned even in most undergraduate textbooks. In spite of the fact that the function is infinitely differentiable, the common procedure of (uniformly) interpolating it with polynomials that use equally spaced points in intervals of suitable length centered at zero has been proven to be an impossible task. In this article, the authors present a proof for the reasons behind the failure of the usual polynomial interpolation of the Runge function which is complete and accessible to undergraduate students with some background in real and numerical analysis. The main idea of the proof is from Isaacson and Keller's work and its presentation is in a self-contained form which is broken down in detailed and easy-to-follow steps. (Contains 4 figures.) (ERIC).
Anmerkungen	MATYC Journal Inc. Mathematics and Computer Education, P.O. Box 158, Old Bethpage, NY 11804. Tel: 516-822-5475; Web site: http://www.macejournal.org
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10