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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 f-p k , with k f-p k = sup x [-1 , 1] | f ( x )-p ( x ) | . (a) Given f ( x ) = x n +1 , nd p n such that k f-p 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 f-p in poly-nomial interpolation. 1...
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- Spring '11
- Numerical Analysis