# hw5 - Assignment #5: Errors in Polynomial Interpolation;...

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Assignment #5: Errors in Polynomial Interpolation; Estimating Derivatives and Richardson Extrapolation Due date: Wednesday, October 20, 2010 (10:10am) For full credit you must show all of your work. 1. Using Matlab, write a progam that can be used to determine, evaluate and plot a polynomial that interpolates the Runge function f ( x ) = (1 + x 2 ) " 1 using n nodes that are evenly spaced over the interval [– a , a ], including the endpoints, where n and a are variables that are initialized at the beginning of your program, allowing them to be easily modified. Show the results of running this program using n = 5, 9, and 13 and a = 3. Following the example pseudocode given on page 138 of our textbook, compute and display an indication of the magnitude of the error that arises at points ¼ , ½ and ¾ of the way between the nodes when using the interpolating polynomial to approximate the function. Please turn in: a) your code; b) a plot that shows the polynomials you derived, and the locations of the nodes, superimposed over a plot of the Runge function; and c) a list or table of the difference between the values taken by the interpolating polynomial and by the Runge function at the points ¼ , ½ and ¾ of the way between the nodes where the two agree.

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## This note was uploaded on 11/29/2010 for the course CSCI cs taught by Professor Intern during the Fall '10 term at Minnesota.

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hw5 - Assignment #5: Errors in Polynomial Interpolation;...

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