Behaviour of stability tests for two-dimensional digital recursive filters when faced with rounding errors

In this paper, the behaviour of four recent algorithms, which test the stability of two-dimensional (2-D) real recursive filters, are compared when faced with rounding errors in floating point arithmetic. Experimental results, comparing the data given by these algorithms when they are implemented either in floating point arithmetic, or with infinite precision in formal calculus, are presented. It appears with this comparison, that this behaviour is a very important point for choosing such an algorithm among all the existing ones.