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Author: Numerically-Stable

Numerical Methods/GramSchmidt.m

@@ -0,0 +1,12 @@
+function U = GramSchmidt(V)
+    [n, k] = size(V);
+    U = zeros(n,k);
+    U(:,1) = V(:,1) / norm(V(:,1));
+    for i = 2:k
+        U(:,i) = V(:,i);
+        for j = 1:i-1
+            U(:,i) = U(:,i) - (U(:,j)'*U(:,i)) * U(:,j);
+        end
+        U(:,i) = U(:,i) / norm(U(:,i));
+    end
+end

Numerical Methods/ModifiedGramSchmidt.m

@@ -0,0 +1,16 @@
+function U = ModifiedGramSchmidt(V)
+    [n, k] = size(V);
+    U = zeros(n,k);
+    U(:,1) = V(:,1) / norm(V(:,1));
+    for i = 2:k
+        V_k = V(:,i);
+        for j = 1:i-1
+            if j==1
+                U_k = V_k - (U(:,j)'*V_k) * U(:,j);
+            else
+                U_k = U_k - (U(:,j)'*U_k) * U(:,j);
+            end            
+        end
+        U(:,i) = U_k / norm(U_k);
+    end
+end