MATLAB: What is the difference between “while” and “for” in this program

for while loop

This is a matlab program of column principal element Gauss elimination method:
function GEpiv(A,b)
[m,n]=size(A);
nb=n+1;
Ab=[A,b];
for i=1:m-1
    [pivot,p]=max(abs(Ab(i:m,i)));
    ip=p+i-1;
    if ip ~=i
        Ab([i ip],:)=Ab([ip i],:);
    end
    pivot=Ab(i,i);
    for k=i+1:m
        Ab(k,i:nb)=Ab(k,i:nb)-(Ab(k,i)/pivot)*Ab(i,i:nb);
    end
end
x=zeros(n,1);
x(n)=Ab(n,nb)/Ab(n,n);
% for i=n-1:1
%     x(i)=(Ab(i,nb)-Ab(i,i+1:n)*x(i+1:n,1))/Ab(i,i);
% end
    
while(i>=1)
    x(i)=(Ab(i,nb)-Ab(i,i+1:n)*x(i+1:n,1))/Ab(i,i);
    i=i-1;
end
for k=1:n
    fprintf('x[%d] = %f\n',k,x(k));
end
A=[2,4,1;2,6,-1;1,5,2];
b=[4;10;2];
Run the program, I wii get
But if I use the for loop , I will get
I think the result should be the same,but in fact they are not,why?

Best Answer

correction and solution:
you should specify that the for goes in the opposite direction
for i=n-1:-1:1
    x(i)=(Ab(i,nb)-Ab(i,i+1:n)*x(i+1:n,1))/Ab(i,i);
end
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