hw8 - Homework 8 Math 471 Fall 2007 Assigned Friday...

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Homework 8 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 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.
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