hw8_solutions - Homework 8 Solutions Math 471, Fall 2007...

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Unformatted text preview: Homework 8 Solutions Math 471, Fall 2007 Assigned: Friday, November 2, 2007 Due: Friday, November 9, 2007 Include a cover page Clearly label all plots using title , xlabel , ylabel , legend Use the subplot command to compare multiple plots Include printouts of all Matlab code, labeled with your name, date, section, etc. 1. (Interpolating Polynomials) The function f ( x ) = 1 / ( x + 1) is given at the four points x = 1, x 1 = 2, x 2 = 3, x 3 = 4. (a) Write the interpolating polynomial in Lagrange form. ( x- 2)( x- 3)( x- 4) (1- 2)(1- 3)(1- 4) 1 2 + ( x- 1)( x- 3)( x- 4) (2- 1)(2- 3)(2- 4) 1 3 + ( x- 1)( x- 2)( x- 4) (3- 1)(3- 2)(3- 4) 1 4 + ( x- 1)( x- 2)( x- 3) (4- 1)(4- 2)(4- 3) 1 5 . (b) Write the interpolating polynomial in Newton form. 1 2- 1 6 ( x- 1) + 1 24 ( x- 1)( x- 2)- 1 120 ( x- 1)( x- 2)( x- 3) (c) Evaluate f (1 . 5) and f (5) using the interpolating polynomial. Which approximate value is more accurate? f (1 . 5) . 403125 , f (5) . 133333 (d) Use the error formula to find an upper bound on the maximum error || f- p 3 || = max 1 x 4 | f ( x )- p 3 ( x ) | . max 1 4 f (4) ( ) 4!...
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hw8_solutions - Homework 8 Solutions Math 471, Fall 2007...

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