Mathematical background

Let $A=((a_{ij}))$ and the Gerschgorin circles defined as the set of $z$ such that:

$$C_i =\vert z-a_{ii}\vert \le \sum_j \vert a_{ji}\vert, j \not= i$$

The roots of the characteristic polynomial are enclosed in the union of the $C_i$. Furthermore if a circle has no intersection with the other circles, then this circle contains one root of the polynomial. This allow for a fast determination of bounds for the real roots of the polynomial.