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format long

l=1/2;

u=1/3;

I=[1,0,0;0,1,0;0,0,1];

A=[4,3,3;2,4,1;3,1,2];

B=det(A)*inv(A);

G_1=[1/3,0,0;0,1/2,0;0,0,1];

G_2=[1/4,0,0;0,1/5,0;0,0,1/6];

T=[1,0,0;0,1,0;0,0,1];

F = [1/2,0,0;0,1/2,0;0,0,1/2];

i=1;

x(1) =1;

y(1) =1;

z(1) =1;

X_i=[x(i);y(i);z(i)];

for i = 1:100

a_i = 1/i^(1/2);

t = 1/5;

Z_i = X_i-t*[(I-inv(I+l*G_1))*X_i + B*((I-inv(I+u*G_2)))*A*X_i];

i = i+1;

X_i = a_i*F*X_i+(1-a_i)*T*Z_i

E(i) = norm(X_i);

L(i) = ((x(i+1) - x(i))^3 + (y(i+1) - y(i))^3 + (z(i+1) - z(i))^3)^(1/3); % main problem is here

end

n=[2:1:100];

plot(n,E(n))

Geoff Hayes
on 18 Nov 2020

feeroz - you never update your x, y, and z after their initialization, so perhaps you are intending to use X_i instead. Try the following which may be what you want

X_i = zeros(3,101);

X_i(:,1) = [1; 1; 1];

for i = 1:100

a_i = 1/i^(1/2);

t = 1/5;

Z_i = X_i(:,i)-t*[(I-inv(I+l*G_1))*X_i(:,i) + B*((I-inv(I+u*G_2)))*A*X_i(:,i)];

X_i(:,i+1) = a_i*F*X_i(:,i)+(1-a_i)*T*Z_i;

E(i) = norm(X_i(:,i+1));

L(i) = ((X_i(1,i+1) - X_i(1,i))^3 + (X_i(2,i+1) - X_i(2,i))^3 + (X_i(3,i+1) - X_i(3,i))^3)^(1/3); % main problem is here

end

In the above, we pre-size the X_i array which we updated on each iteration of the loop. We then use that instead of the x, y and z when updating L(i). Note that you could pre-size E and L too.

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