The IsConvergent command determines whether the iterative approximation to the linear system A.x=b, using meth as the approximation method, converges to a unique solution or not, for any initial approximate.

The IsConvergent command returns true or false depending on whether the method and system converge to a unique solution or not.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{NumericalAnalysis}\right]\right)\:$

$A≔\mathrm{Matrix}\left(\left[\left[1.3\,1.4\,5.3\right]\,\left[3.4\,7.7\,3.1\right]\,\left[4.3\,7.4\,0.2\right]\right]\right)$

$A≔\left[\begin{array}{ccc}1.3& 1.4& 5.3\\ 3.4& 7.7& 3.1\\ 4.3& 7.4& 0.2\end{array}\right]$

$\mathrm{IsConvergent}\left(A\,\mathrm{method}=\mathrm{gaussseidel}\right)$

$\mathrm{false}$

$\mathrm{IsConvergent}\left(A\,\mathrm{method}=\mathrm{jacobi}\right)$

$\mathrm{false}$

$B≔\mathrm{Matrix}\left(\left[\left[1\,0\right]\,\left[0\,1\right]\right]\right)$

$B≔\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

$\mathrm{IsConvergent}\left(B\,\mathrm{method}=\mathrm{gaussseidel}\right)$

$\mathrm{true}$

$\mathrm{IsConvergent}\left(B\,\mathrm{method}=\mathrm{jacobi}\right)$

$\mathrm{true}$

$\mathrm{IsConvergent}\left(B\,\mathrm{method}=\mathrm{SOR}\left(1.25\right)\right)$

$\mathrm{true}$