sols_wk9

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Homework 9 due Thursday December 9 before 13:30 in corre-sponding group folder on door of oﬃce 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 ) ....
View Full Document

## This note was uploaded on 02/09/2011 for the course MATH 2051 taught by Professor Dr.a.wacher during the Fall '11 term at Durham.

Ask a homework question - tutors are online