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Unformatted text preview: large as n becomes large is to consider the error term for polynomial interpolation ∏ = + − + = − n i i n n x x n f x P x f ) 1 ( ) ( )! 1 ( ) ( ) ( ) ( ξ . As n → ∞ , it can be shown that ∞ → − ) ( ) ( x P x f n (at some points x in [ − 1, 1] ). Note: if the points of interpolation are not constrained to be equally spaced, then it is possible to choose the points of interpolation x i so that ) ( ) ( lim x f x P n n = ∞ → . However, there is no known rule that indicates how to choose appropriate points of interpolation x i to guarantee such convergence of the interpolating polynomials for arbitrary continuous functions ) ( x f ....
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 Spring '08
 Olesky
 Computer Science, Numerical Analysis, Polynomial interpolation, Runge's phenomenon, interpolation xi

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