10.2 (a) Write a wl-commented MaTLAB function program mysolvecheck with input a

Question

10.2 (a) Write a wl-commented MaTLAB function program mysolvecheck with input a number n that makes a random n × n matrix A and a random vector b, solves the linear system Ax-b, calculates the scalar residual Ax bll, and outputs that number as r. (b) Write a well-commented MATLAB script program that calls mysolvecheck 10 times each for n 10, 50, 100, 500, and 1000, records and averages the results and makes a log-log plot of the average e vs. n. Increase the maximum n until the program stops running within 5 minutes. Turn in the plot and the two prograns.

Explanation / Answer

function r = mysolvecheck(n)
    A = -100 + rand(n,n) * 200;
    B = -100 + rand(n,1) * 200;
    X = linsolve(A, B);
    r = norm( (A*X - B), Inf);
end

nValues = [10, 50, 100, 500, 1000];
r = [];

for i=1:length(nValues)
    n = nValues(i);
    rSum = 0;
    for j = 1:10
        rSum = rSum + mysolvecheck(n);
    end  
    r(i) = rSum /10;
end

loglog(nValues, r, '-s');
title('Linear Equations');
xlabel("n values"); ylabel("residual values");

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