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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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 Winter '08
 LinZhi
 Math, Numerical Analysis

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