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Runge Function

The Runge function is the rational function

f(x)=1/(1+25x^2),

usually considered on the interval [-1,1] as a test of polynomial interpolation. It is analytic on the real interval, but interpolation at equally spaced nodes exhibits the Runge phenomenon. Interpolation at Chebyshev nodes instead converges rapidly (Trefethen 2019).

See also

Chebyshev Nodes, Polynomial Interpolation, Runge Phenomenon

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References

Runge, C. "Ueber empirische Funktionen und die Interpolation zwischen äquidistanten Ordinaten." Z. Math. Phys. 46, 224-243, 1901.Trefethen, L. N. "The Runge Phenomenon." §4.7 in Chebfun Guide. Rev. May 2019. https://www.chebfun.org/docs/guide/guide04.html.

Cite this as:

Weisstein, Eric W. "Runge Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RungeFunction.html

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