Fall2011-HW10

# Fall2011-HW10 - -1 , 1]. You may use the Matlab scripts...

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Homework 10 Math 371, Fall 2011 Assigned: Thursday, November 17, 2011 Due: Thursday, December 1, 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) (Chebyshev polynomials) Do problem #3 on page 385 of Bradie. (2) (Convergence of functions) Recall that the n th order set of Chebyshev nodes consists of the points x j = cos( πj/n ) for j = 0 , 1 ,...,n . (a) Write a Matlab program that computes the n th degree polynomial interpolant p n of an input function f at the Chebyshev nodes and plots p n on the interval [
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Unformatted text preview: -1 , 1]. You may use the Matlab scripts supplied with the previous homework. (b) Apply your program to the functions f ( x ) = | x | and g ( x ) = sign( x ) for each n = 4 , 8 , 16. For each function, report whether the interpolants appear to be converging on [-1 , 1]. If so, is the convergence pointwise or uniform? (3) Piecewise Linear Interpolation) Use the error theorem on p. 390 to compute an upper bound on the pointwise error from interpolating f ( x ) = e-x 2 on the interval [-4 , 4] with piecewise linear functions at the points-4,-2, 0, 2, and 4. (4) (Cubic Spline Interpolation) P. 403 #10, P. 404 #15. 1...
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## This note was uploaded on 12/16/2011 for the course MATH 371 taught by Professor Krasny during the Fall '08 term at University of Michigan.

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