Talk:Jacobi method

Algorithm

In the Algorithm section, the formula between the end of the j loop and the end of the i loop cannot possibly work. In most languages you can't have a power calculation on the left side of the equals sign. This needs to be revised to a statement that will actually work. — Preceding unsigned comment added by Statguy1 (talk • contribs) 03:45, 28 April 2015 (UTC)

The left hand side of that formula is not a power calculation. $x_{i}^{(k+1)}$ is standard notation in numerical methods for the k + 1 iteration of x sub i. Unfortunately, this notation does not seem to be defined in any of the Wikipedia articles on numerical methods, although it should be. For example, it should be defined in Iterative method, Gauss-Seidel method, Successive over-relaxation and this article. — Anita5192 (talk) 05:48, 28 April 2015 (UTC)

I just inserted an explanation of the notation in this article and in the three other articles I mentioned above. Hopefully this will make the articles more clear. — Anita5192 (talk) 06:28, 28 April 2015 (UTC)

Python (2 and 3)

Nice to see script! Very small comment - it runs in both 2 and 3, maybe no need to say "3"? — Preceding unsigned comment added by Synecdodave (talk • contribs) 04:42, 3 July 2015 (UTC)

You are right. I removed the version number. Gromobir (talk) 13:46, 22 September 2015 (UTC)

Convergence in the symmetric positive definite case

The last example given in the convergence section is not PD matrix, moreover, jacobi method converges for all pd matrices— Preceding unsigned comment added by 14.139.222.72 (talk) 20:51, 02 May 2019 (UTC)

Are you sure about convergence for all pd matrices?

$A={\begin{pmatrix}29&2&1\\2&6&1\\1&1&0.2\end{pmatrix}}\quad \Rightarrow \quad D^{-1}R={\begin{pmatrix}0&{\frac {2}{29}}&{\frac {1}{29}}\\{\frac {1}{3}}&0&{\frac {1}{6}}\\5&5&0\end{pmatrix}}\quad \Rightarrow \quad \rho (D^{-1}R)\approx 1.0661\,.$

Franc Pasc (talk) 18:56, 8 September 2019 (UTC)

Standard conversion condition by spectral radius given makes no sense

All terms in the given convergence condition are constant over iterations. How can it be a conversion condition if the latest estimate for **x** is not part of the formula?

Could we have a derivation of the solution?

It is completely unknown to me how we arrived to the solution of the Jacobi iteration algorithm. Could we include a section to a derivation? MartensCedric (talk) 19:18, 21 October 2024 (UTC)

If you meant "Where did the method come from?" one way of deriving the method is with a matrix splitting. Proving that it converges is another matter. For some methods, this can be proved. Other methods are used simply because they converge to the correct solution. For more information, you might try the See-also links, the reference, and the external links.—Anita5192 (talk) 19:41, 21 October 2024 (UTC)