Commit dfee15ac by Conor McCoid

### Extrap: test of v2 as underdetermined system solve

parent 6f691b6b
 % 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') ... ...
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