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Unformatted text preview: (c) What is the expected order of a composite integration method based upon the formula with coecients derived in (a)? 4. Let n denote the space of all polynomials of degree n . Given a function f dened on [1 , 1], we denote dist( f, n ) = inf p n k fp k , with k fp k = sup x [1 , 1]  f ( x )p ( x )  . (a) Given f ( x ) = x n +1 , nd p n such that k fp k = dist( f, n ) . (2) Prove that your p indeed satises (2). (b) For the same f , compute dist( f, n ). (c) With f and p as above, discuss briey the use of the error function fp in polynomial interpolation. 1...
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 Spring '11
 NA
 Numerical Analysis

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