Extrap: added GMRES comparison to linear FPI example

Research/Extrapolation methods/Code/ALGO_extrap_MPE_v1_20211022.m

-function x_out=ALGO_extrap_MPE_v1_20211022(F,X)
+function [x_out,r_out]=ALGO_extrap_MPE_v1_20211022(F,X)
 % MPE performs minimal polynomial extrapolation using Arnoldi iteration
 
 [d,k] = size(F);
 q0 = F(:,1); Hinv = 1/norm(q0); q0 = Hinv*q0;
 Q = zeros(d,k); Q(:,1) = q0; x_out=zeros(d,k); x_out(:,1)= X(:,1);
+r_out=zeros(1,k); r_out(1)=norm(F(:,1));
 for j=2:k
     Q(:,j) = F(:,j);
     h = zeros(j-1,1);
@@ -14,6 +15,7 @@ for j=2:k
     hj = norm(Q(:,j)); Q(:,j)  = Q(:,j)/hj;
     Hinv = [Hinv, -Hinv*h/hj; zeros(1,j-1), 1/hj];
     u=Hinv(:,end); u=u/sum(u); x_out(:,j)=X(:,1:j)*u;
+    r_out(j)=norm(F(:,1:j)*u);
 end
 % if nargin==1
 %     x_out=x_out(:,end);

Research/Extrapolation methods/Code/EX_extrap_linearFPI_v1_20211022.m

@@ -9,15 +9,28 @@ for i=1:n
 end
 F = X(:,2:end) - X(:,1:n);
 
-x_out = ALGO_extrap_MPE_v1_20211022(F,X(:,1:n));
+[x_out,r_out] = ALGO_extrap_MPE_v1_20211022(F,X(:,1:n));
 x = x_out(:,end);
 Error_abs= norm(x - x_true)
 Error_rel= Error_abs/norm(x_true)
 Residual = norm(A*x + b - x)
 
-Error_list = zeros(1,n);
+Error_list = zeros(1,n); res_MPE = zeros(1,n);
 for i=1:n
     Error_list(i) = norm(x_out(:,i) - x_true);
+    res_MPE(i) = norm(A*x_out(:,i) + b - x_out(:,i));
 end
 
-semilogy(1:n,Error_list,'b*--')
\ No newline at end of file
+[x_GMRES,~,~,~,res_GMRES]=gmres(A-eye(d),-b);
+
+figure(1)
+semilogy(1:n,Error_list,'b*--')
+xlabel('Iteration')
+ylabel('Error in solution')
+title('Error vs iteration')
+
+figure(2)
+semilogy(1:n,res_MPE,'b*--',1:length(res_GMRES),res_GMRES,'ro')
+xlabel('Iteration')
+ylabel('Residual')
+title('Residual vs iteration')
\ No newline at end of file