472F16hw4 - Math 472 F 2016 Homework 4 Due Friday Nov 11 at...

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Math 472, F 2016, Homework 4 Due Friday Nov 11 at 4 pm Include a cover page Always clearly label all plots (title, x -label, y -label and legend) Use the subplot command from MATLAB when comparing 2 or more plots to make comparisons easier and to save paper. Include all of your MATLAB code. Place a comment at the top of each submitted function or script including the name of the function or script, the date and MATH 472. (1) (a) As described in class, write a MATLAB function file which com- putes the LU factorization of an N × N tri-diagonal matrix A . The input for the MATLAB function should be an N dimen- sional vector a and two N - 1 dimensional vectors e and d . The entries of a form the diagonal entries of A , the entries of e the lower triangular entries of A , and the entries of d the upper triangular. The output of the function file should be L and U . (b) Use your program to compute the LU factorization of the 6 × 6 matrix 7 - 4 0 0 0 0 - 4 3 8 0 0 0 0 3 6 5 0 0 0 0 6 - 3 - 6 0 0 0 0 5 5 - 2 0 0 0 0 - 3 8 . (2) Let N > 5 and m = m N be the largest integer less than or equal to N
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