Hubert Matrices
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C) The famous Hubert matrices are given by Hij= 1/(i +j - 1). The n x n Hilbert matrix Hn is easily produced in MATLAB using hilb(n). Assume the true solution of H,x = b for a given n is x = [1.. .. , 1]^T. Hence the righthand side b is simply the row sums of H, and b is easily computed in MATLAB using b=sum(hilb(n) 9'. Use your codes mylu.m and lusolve.m to solve the system Hnx = b for i. = 5, 10, 15, 20. For each n, using the oo ? norm, compute the relative error and the relative residual. Discuss what is happening here. You may find it useful to look at the cond command in MATLAB.
(You do not have to use MATLAB to deal with this problem.)
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Hubert Matrices are investigated.
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