(2) Realize the experiment 2: Classical vs. Modified Gram-Schmidt on page 65-66, by writing the Algorithm 7.1 and Algorithm 8.1 as matlab functions.

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function gs()
% Comparing classic Gram-Schmidt vs Modifies G-S

% Creating a random matrix with singular values spanning large log range
N = 80;
nn = 1:N;
[U,X] = qr(randn(N));
[V,X] = qr(randn(N));
S = diag(2.^(-nn));

% testing the two versions of GS

% Plot comparison to see who breaks first
% we plot absolute values because of possible numeric errors
f = figure(1);
semilogy(nn,abs(diag(rc)),'o', nn,abs(diag(rm)),'x');
legend('Classic GS','Modified GS');
ylabel('Diagonal elements of R');
set(gca, 'XGrid','On');   
set(gca, 'YGrid','On')...

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