Unformatted text preview: f ( x ) = x sin x is approximated by a polynomial of degree nine that interpolates our function f at ten points in the interval [0 , 1], then show that the error is less then 30 . 8 × 10-7 on this interval. ( 8 points ) 5.4. (Bonus) Let x , x 1 , x 2 , . . . , x n be arbitrary integers, x < x 1 < x 2 . . . < x n . Show that every polynomial of n th degree of the form x n + a 1 x n-1 + a 2 x n-2 + . . . + a n assumes at the points x , x 1 , x 2 , . . . , x n values, at least one of which is of absolute value ≥ n ! 2 n . ( 10 bonus points ) Due: 12.03.10, at 3 pm (in the mailbox labeled Linsen in the entrance hall of Res.I )...
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- Spring '10
- Numerical Analysis, Polynomial interpolation, Prof. Dr. Lars Linsen, Dr. Lars Linsen