function [X,Y] = cr_struct(R1,R2,R3,R4,R5,R6)
% [X,Y]=CR_STRUCT(R1,R2,R3,R4,R5,R6) applies CR to the structured UQME 
% obtained by the simple tranformation
% R1, R2, R3, R4, R5, R6: initial matrices
% X, Y: limit of the sequence (X_k) and (Y_k), respectively
tol = 1e-13;
kmax = 30;
n = size(R2,2);
RR1 = R1; RR2 = R2; RR3 = R3; RR5 = R5;
% CR step
err = 1;
k = 0;
while err > tol && k < kmax
    S = R5 + R4*R3;
    W = S\[R2+R4*R1,R6];
    Y = W(:,1:n);
    Z = W(:,n+1:end);
    X = R3*Y - R1;
    T = R3*Z;
    R3 = R3 - R1*T;
    R4 = R4 - R6*Y;
    R5 = R5 - R2*T;
    R1 = -R1*X;
    R2 = -R2*X;
    R6 = -R6*Z;
    k = k+1;
    err = min(norm(R6,1),max(norm(R1,1),norm(R2,1)));
end
X = -(RR5 + R4*RR3)\(RR2 + R4*RR1);
Y = R3/R5;
if k == kmax
   disp('Warning: reached the maximum number of iterations')
enD