Reliable numerical methods for polynomial matrix triangularization

Numerical procedures are proposed for triangularizing polynomial matrices over the eld of polynomial fractions and over the ring of polynomials. They are based on two standard polynomial techniques: Sylvester matrices and interpolation. In contrast to other triangularization methods, the algorithms described in this paper only rely on well-worked numerically reliable tools. They can also be used for greatest common divisor extraction, polynomial rank evaluation or polynomial null-space computation.