0

I reedited the question:

We want to use Jacobi method to solve the following system:

$$ \begin{bmatrix} \pi^2 & -1 & 0 & 0 \\ -1 & \pi^2 & -1 & 0 \\ 0 & -1 & \pi^2 & -1 \\ 0 & 0 & -1 & \pi^2 \end{bmatrix} \times \begin{bmatrix} x_1 \\ x_2 \\ x_3 \\ x_4 \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \end{bmatrix} $$

Be $x^{(*)}$ the solution of the system. Use the estimative

$$ ||x^{(k)} - x^{(*)}||_\infty \leq \frac{\sigma^k}{1-\sigma}||x^{(1)}-x^{(0)}||_\infty $$

to get the number of iterations needed to obtain an error less than $\epsilon = 10^{-8}$, beginning at

\begin{bmatrix} 0 \\ 0 \\ 0 \\ 0 \end{bmatrix}

Silas
  • 133
  • The problem statement is ill posed. What do you mean by converges, what norm? What type of error do you mean? Also, the short answer is: in general, you won't know exactly. Sometimes you can give an upper bound if your problem is small and/or your relaxation update matrices are nice. – Merkh Aug 16 '17 at 21:52
  • I restated the question. Does it make sense? – Silas Aug 16 '17 at 22:59
  • Have you calculated $σ$ and $x^{(1)}$ to evaluate the right side of the estimate? That is what I would try first, since it is the only information / estimate provided. – P. Siehr Aug 17 '17 at 07:41

0 Answers0