Assign1_1_c.m

[n,m] = size(A1); %size of matrix
options = optimoptions('linprog','Algorithm','dual-simplex'); % setting dual-simplex for solver

result1_L1 = linprog([zeros(m,1);ones(n,1)],[+A1,-eye(n);-A1,-eye(n)],[b1;-b1]); % solving L1 norm, see http://math.stackexchange.com/questions/81150/solving-ax-b-under-l-1-ax-b-minimization
result1_L1_x = result1_L1(1:m); % result L1-norm X vector
res1_L1_norm = norm(A1*result1_L1_x - b1, 1);  %residuals L1 norm

result1_Linf = linprog([zeros(m,1);ones(1,1)],[+A1,-ones(n,1);-A1,-ones(n,1)],[b1;-b1]); % solving Linf norm minimization
result1_Linf_x = result1_L1inf(1:m); % result L1-norm X vector
res1_Linf_norm = norm(A1*result1_Linf_x - b1, 1);  %residuals Linf norm

result1_L2 = linsolve(A1.' * A1, A1.' * b1);
res1_L2 = norm(A1*result1_L2 - b1, 2);