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Fall2011-HW9

# Fall2011-HW9 - Homework 9 Math 371 Fall 2011 Assigned...

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Homework 9 Math 371, Fall 2011 Assigned: Thursday, November 10, 2011 Due: Thursday, November 17, 2011 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, and section. Add 12 for page numbers in the international edition. (1) (Interpolating Polynomials) The function f ( x ) = 1 / ( x + 1) is given at the four points x 0 = 1 , x 1 = 2 , x 2 = 3 , x 3 = 4 . (a) Write the interpolating polynomial in Lagrange form. (b) Write the interpolating polynomial in Newton form. (c) Evaluate f (1 . 5) and f (5) using the interpolating polynomial. Which approximate value is more accurate? (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 ) | . (2) (Choice of Interpolation Points) This question investigates how different interpolation points affect the accuracy of the interpolation. Let f ( x ) = 1 20 x 2 +1 . (a) Compute and plot the interpolating polynomial for f ( x ) using the equally spaced points x 0 = - 1 , x 1 = 0 , x 2 = 1 . (b) The third Chebyshev polynomial is
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