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A note on Lagrange interpolation for |x|λ at equidistant nodes

Published online by Cambridge University Press:  17 April 2009

Michael I. Ganzburg  and
Michael Revers
Michael I. Ganzburg
Affiliation:
Department of Mathematics, Hampton University, Hampton, VA 23668, United States of America, e-mail: michael.ganzburg@hamptonu.edu
Michael Revers
Affiliation:
Department of Mathematics, University Salzburg, Hellbrunnerstrasse 34, A-5020 Salzburg, Austria e-mail: michael.revers@sbg.ac.at Internet: www.michael.revers.at
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In this note, we discuss the exceptional set E ⊆ [−1, 1] of points x0 satisfying the inequality where λ > 0, λ ≠ 2, 4, … and Ln(fλ,.) is the Lagrange interpolation polynomial of degree at most n to fλ(x):= |x|λ on the interval [−1, 1] associated with the equidistant nodes. It is known that E has Lebesgue measure zero. Here we show that E contains infinite families of rational and irrational numbers.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 3 , December 2004 , pp. 475 - 480
Copyright
Copyright © Australian Mathematical Society 2004

References

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