CSC_349_HANDOUT#23 - large as n becomes large is to...

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1 COMPUTER SCIENCE 349A Handout Number 23 THE RUNGE PHENOMENON The following example is the classical example to illustrate the oscillatory nature and thus the unsuitability of high order interpolating polynomials. It is due to Runge in 1901. Consider the problem of interpolating f ( x ) = 1 1 + 25 x 2 on the interval [ 1, 1] at n + 1 equally-spaced points x i by the interpolating polynomial P n ( x ). In the figure below, the graphs of ) ( and ) ( ), ( 20 5 x P x P x f are shown. f(x) degree 5 degree 20 x
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