Checking the Congruence between Accretive Matrices

We call a finite computational process using only arithmetic operations a rational algorithm. A rational algorithm that is able to check the congruence between arbitrary complex matrices $A$ and $B$ is currently not known. The situation may be different if $A$ and $B$ belong to a certain class of special matrices. For instance, there exist rational algorithms for the case where both matrices are Hermitian or unitary. In this paper, rational algorithms for checking the congruence between accretive or dissipative $A$ and $B$ are proposed.