sols_wk9 - Homework 9 due Thursday December 9 before 13:30...

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Unformatted text preview: Homework 9 due Thursday December 9 before 13:30 in corre-sponding group folder on door of oce CM110 1. Find the Hermite interpolating cubic for 1 / (1 + x 2 ), based on the values of this function and its derivative at 1 and 1. We use the Hermite interpolation formula for f ( x ) = (1+ x 2 )-1 at the nodes x = 1 and x 1 = 1. So f ( x ) = 2 x (1 + x 2 )-2 and f ( 1) = 1 / 2, f ( 1) = 1 / 2. Taking x = 1 and x 1 = 1, calculations reveal that h ( x ) = (1 x 2 )(1 x ) 4 , h 1 ( x ) = ( x 2 1)(1 + x ) 4 , h ( x ) = ( x + 2)(1 x ) 2 4 , h 1 ( x ) = (2 x )(1 + x ) 2 4 . So using the Hermite interpolation polynomial p 3 ( x ) = 1 2 (1 x 2 )(1 x ) 4 1 2 ( x 2 1)(1 + x ) 4 + 1 2 ( x + 2)(1 x ) 2 4 + 1 2 (2 x )(1 + x ) 2 4 = 1 4 ( 3 x 2 ) ....
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