Extrap: playing around with Householder version for overdetermined systems

Research/Extrapolation methods/Code/ALGO_extrap_MPE_v3_20211119.m

@@ -6,13 +6,19 @@ function [x_out,r_out]=ALGO_extrap_MPE_v3_20211119(F,X)
 R=F; H=zeros(d,k); %I=eye(d); Q=I;
 x_out=zeros(d,k); r_out = zeros(k,1);
 x_out(:,1)=X(:,1);r_out(1)=norm(F(:,1));
-for i=1:min(d,k)
-    w = SUB_extrap_Householder_v1_20211119(R(:,i),i);
+for i=1:k
+    if i<=d
+        w = SUB_extrap_Householder_v1_20211119(R(:,i),i);
 %     Q = Q - 2*Q*(w*w');
-    R = R - 2*(w*w')*R;
+        R = R - 2*(w*w')*R;
+    end
     if i>1
-        H(1:i-1,i-1)=R(1:i-1,i)-R(1:i-1,i-1); H(i,i-1)=R(i,i);
-        u = zeros(i-1,1); u(1)=-R(1,1); u=H(1:i-1,1:i-1)\u;
+        ind=1:min(i-1,d);
+        H(ind,i-1)=R(ind,i)-R(ind,i-1);
+        if i<=d
+            H(i,i-1)=R(i,i);
+        end
+        u = zeros(min(i-1,d),1); u(1)=-R(1,1); u=H(ind,1:i-1)\u;
         u = [1;u] - [u;0];
         x_out(:,i) = X(:,1:i)*u;
         r_out(i) = norm(F(:,1:i)*u);

Research/Extrapolation methods/Code/EX_extrap_linearFPI_v1_20211022.m

 % Example - Extrapolation: fixed point iteration on linear function
 %   solve the equation x = Ax + b for random A and b
 
-d = 40; n=2*d;
+d = 10; n=2*d;
 A = rand(d); 
-A = A/norm(A); 
+% A = A/norm(A); 
 b = rand(d,1); x_true = -(A - eye(d)) \ b;
 X = b;
 for i=1:n