First of all 0,01 should be 0.01. Secondly, i=1; should be outside the while loop, else the value of i is reset every loop. I also fixed your display commands:
clc;clear; format ('long' , 'g'); x1(1)=1;x2(1)=1; x3(1)=1;x4(1)=1; error=1;
i=1;
while error >=0.01
x1(i+1)=(-23+x2(i)-x3(i)+2*x4(i))/4;
x3(i+1)=((2*x1(i+1)-6*x2(i)+3*x4(i)+21));
x2(i+1)=(-x1(i+1)+11+5*x3(i+1)+x4(i))/2;
x4(i+1)=(22+x1(i+1)-2*x2(i+1)+3*x3(i+1))/6;
error_x1(i+1)=abs((x1(i+1)-x1(i)))/x1(i+1);
error_x3(i+1)=abs((x3(i+1)-x3(i)))/x3(i+1);
error_x2(i+1)=abs((x2(i+1)-x2(i)))/x2(i+1);
error_x4(i+1)=abs((x4(i+1)-x4(i)))/x4(i+1);
A=[error_x1 ;error_x3 ;error_x2;error_x4];
error=max(A);
i=i+1;
end
disp ( ' x1(i+1) error(%) ')
disp([x1(end) error_x1(end)])
disp ( ' x3(i+1) error(%)')
disp([x2(end) error_x2(end)])
disp ( ' x2(i+1) error(%)')
disp([x3(end) error_x3(end)])
disp ( ' x4(i+1) error(%)')
disp([x4(end) error_x4(end)])
