How can I stop My Gauss-Seidel loop when the if condition is met.

3 次查看（过去 30 天）
Hieu Nguyen
Hieu Nguyen 2017-3-3
编辑： Bruno Luong 2018-9-30
D = diag(diag(A));
L = tril(-A,-1);
U = triu(-A,1);
%transition matrix and constant vector used for iterations
Tg = inv(D-L)*U;
cg = inv(D-L)*b;
tol = 1e-05;
k = 1;
x = zeros(n,1); %starting vector
N=100;
while k <= N
x(:,k+1) = Tg*(x(:,k)) + cg;
if ((norm(x(:,k+1)-x(:,k),'inf'))/(norm(x(:,k+1),'inf'))) < tol
break;
end;
k = k+1;
end;
disp(['Iteration ' num2str(k)]);
plot(x,'-o');
end
Hello, I tried to stop my iteration when ever my condition is met: infinity norm of (x(k+1) - x(k)) / infinity norm of(x(k)) < tol. Somehow, my loop will keep working until it reaches the end of my designated N. Please help me fix my while loop. Thank you.
  2 个评论
Darshan Ramakant Bhat
Darshan Ramakant Bhat 2017-3-6
Can you please put the complete code. Lots of values are missing, cannot run this script in the MATLAB editor. Also put sample test matrix 'A' in which you are getting the error. Without the data it is hard to debug.
Regards
Darshan
Bruno Luong
Bruno Luong 2018-9-30
编辑：Bruno Luong 2018-9-30
May be it's a slow convergence and you need more iterations.
My suggestion: display
norm(x(:,k+1)-x(:,k),'inf')
and
norm(x(:,k+1),'inf')
along the iterations and see how they evolve.

请先登录，再进行评论。

请先登录，再回答此问题。

回答（1 个）

Jan
Jan 2017-3-6
The INF-norm is not sufficient here:
if ((norm(x(:,k+1)-x(:,k),'inf'))/(norm(x(:,k+1),'inf'))) < tol
What about:
if max(abs(x(:,k+1) - x(:,k)) ./ abs(x(:,k+1))) < tol
  2 个评论
Leah Youngquist
Leah Youngquist 2018-9-29
Can I ask why the infinity norm is 'insufficient' here? Your solution was exactly what I needed for my problem, but I'm not sure I understand why! ((sorry if this kind of thing is against the Matlab forum rules, I'm a fresh coding baby ha-ha!))
Bruno Luong
Bruno Luong 2018-9-30
编辑：Bruno Luong 2018-9-30
Agree: Jan's expression compute exactly the same than Nguyen's expression.

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Mathematics 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by