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October 24th, 2011, 04:44 PM   #1
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PROOF HELP NUMERICAL ANALYSIS!!!

(a) Prove that the polynomial of degree  n which interpolates f(x) at n+1 distinct
points is f(x) itself in case f(x) is a polynomial of degree  n.

(b) Prove that the kth divided di erence p[x0; x1; : : : ; xk] of a polynomial p(x) of
degree  k is independent of the interpolation points x0; x1; : : : ; xk.

(c) Prove that the kth divided di erence of a polynomial of degree < k is zero.
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