pset_V-06-2 - MMAE 350 D. Rempfer Problem Set V Page 1 of 2...

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Unformatted text preview: MMAE 350 D. Rempfer Problem Set V Page 1 of 2 Due Date: October 23, 2006 1. We want to calculate and compare two di ff erent interpolants of f ( x ) = 1 / (1 + 25 x 2 ) in the interval x [- 1 , 1]. a. Write down the Lagrange interpolating polynomial you obtain for the points ( x i ,f ( x i )), and plot it together with f ( x ), for x i {- 1 ,- . 5 , , . 5 , 1 } , i = , 1 , 2 ,..., 4. b. For the points x i {- 1 ,- . 75 ,- . 5 ,- . 25 , , . 25 , . 5 , . 75 , 1 } , i = , 1 , 2 ,..., 8, derive a linear system of equations describing the coe ffi cients a i of the interpolating polynomial p ( x ) = a + a 1 x + a 2 x 2 + a 3 x 3 + ... . Pick the highest-order polynomial possible. Solve the system of equations, and plot the resulting interpolating polynomial together with the functions from a . Comment on your findings. c. Calculate a cubic-spline interpolant using the same set of points as in a , and then plot the result together with f , following these steps: * The second derivatives of the cubic spline s ( x ) at the nodes are given by the equation ( x i- x i- 1 ) s 00 ( x i- 1 ) + 2( x i + 1- x i- 1 ) s 00 ( x i ) + ( x i + 1- x i ) s 00 (...
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This note was uploaded on 05/04/2008 for the course MMAE 350 taught by Professor Rempher during the Spring '05 term at Illinois Tech.

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pset_V-06-2 - MMAE 350 D. Rempfer Problem Set V Page 1 of 2...

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