Numerical Analysis of Ordinary and Delay Differential Equations by Taketomo Mitsui & Guang-Da Hu

Author:Taketomo Mitsui & Guang-Da Hu
Language: eng
Format: epub
ISBN: 9789811992636
Publisher: Springer Nature Singapore

Then, it can be shown the estimation

holds. This implies that the relative interpolation error has a bound closely equal to . Moreover, it can be proved the identity

(4.15)

holds. The constant , which is determined only by the distribution of the support abscissae (see the definition of !), is called the Lebesgue constant. In fact, for the equidistant case the estimation is known as . This means there should be an interpolated function in whose error with polynomial interpolation explodes when n increases.

The constant has another significance in the polynomial interpolation. Suppose the interpolated function f(x) is slightly perturbed to . Since the interpolation operator is linear, the estimation

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