Extrap: test of v2 as underdetermined system solve

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 = 100; n=2*d;
+d = 5; n=2*d;
 A = rand(d); 
 A = A/norm(A); 
 b = rand(d,1); x_true = -(A - eye(d)) \ b;
@@ -12,8 +12,8 @@ end
 F = X(:,2:end) - X(:,1:n);
 
 [x_v1,r_v1] = ALGO_extrap_MPE_v1_20211022(F,X(:,1:n));
-% [x_v2,r_v2] = ALGO_extrap_MPE_v2_20211029(F,X(:,1:n));
-[x_v2,r_v2] = ALGO_extrap_MPE_v3_20211119(F,X(:,1:n));
+[x_v2,r_v2] = ALGO_extrap_MPE_v2_20211029(F,X(:,1:n));
+% [x_v2,r_v2] = ALGO_extrap_MPE_v3_20211119(F,X(:,1:n));
 x = x_v1(:,end);
 Error_abs= norm(x - x_true)
 Error_rel= Error_abs/norm(x_true)
@@ -25,14 +25,14 @@ Error_v2 = vecnorm(x_v2 - x_true);
 [x_GMRES,~,~,~,res_GMRES]=gmres(A-eye(d),-b,d,eps,d,eye(d),eye(d),X(:,1));
 
 figure(1)
-semilogy(1:n,Error_v1,'b*--',1:d+1,Error_v2,'k.--')
+semilogy(1:n,Error_v1,'b*--',1:length(Error_v2),Error_v2,'k.--')
 xlabel('Iteration')
 ylabel('Error in solution')
 title('Error vs iteration')
 legend('MPE w/ Arnoldi','MPE w/ HH,Givens')
 
 figure(2)
-semilogy(1:n,res_MPE_v1,'b*--',1:d+1,r_v2,'k.--',1:length(res_GMRES),res_GMRES,'ro')
+semilogy(1:n,res_MPE_v1,'b*--',1:length(r_v2),r_v2,'k.--',1:length(res_GMRES),res_GMRES,'ro')
 xlabel('Iteration')
 ylabel('Residual')
 title('Residual vs iteration')