Convergence Criterion (Diagonal Dominant)

Diagonal dominant matrices $[A]$ for the $[A]\{x\}=\{b\}$ is sufficient but not necessary for convergence.

• If the condition is satisfied, convergence is guaranteed, but if the convergence is not met, convergence may still be achieved.

A diagonally dominant matrix is defined to have:

$$\mid a_{ii}\mid >\sum _{j=1;j\ne -i}^n|a_{ij}|$$

Basically, the magnitude of the diagonal for each row is larger than the sum of the magnitudes of all the other entries in the row.