real

lab3_old/GaussNoPivot.m

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+% Modified Gauss Elimination without pivoting
+function x = GaussNoPivot(A,b)
+[m,n]=size(A);
+if m~=n, error('Matrix A must be square'); end
+nb=n+1;
+Aug=[A b];
+for k = 1:n-1
+ for i = k+1:n
+  factor=Aug(i,k)/Aug(k,k);
+  Aug(i,k:nb)=Aug(i,k:nb)-factor*Aug(k,k:nb);
+ end
+end
+x=zeros(n,1);
+x(n)=Aug(n,nb)/Aug(n,n);
+for i = n-1:-1:1
+ x(i)=(Aug(i,nb)-Aug(i,i+1:n)*x(i+1:n))/Aug(i,i);
+end
+end

lab3_old/mylup.m

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+function [L, U, P] = mylup(A)
+[n,~] = size(A);
+C = [A (1:n)'];
+for j = 1:n-1
+ [~, i] = max(abs(C(j:n, j)));
+ i = i + j - 1;
+ if i ~= j
+  C([i j], :) = C([j i], :);
+ end
+ for k = j+1:n
+  C(k, j) = C(k, j)/C(j, j);
+  C(k, j+1:n) = C(k, j+1:n) - C(k, j)*C(j, j+1:n);
+ end
+end
+PP = C(:, end); C = C(:, 1:n);
+L = tril(C, -1) + eye(n); U = triu(C);
+P = eye(n); P = P(PP, :);
+end