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A note on Lagrange interpolation for |x|λ at equidistant nodes
Published online by Cambridge University Press: 17 April 2009
Extract
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.
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- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 70 , Issue 3 , December 2004 , pp. 475 - 480
- Copyright
- Copyright © Australian Mathematical Society 2004
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