Reliable Numerical Methods for Polynomial Matrix Triangularization

: Numerical procedures are proposed for triangularizing polynomial matrices over the field 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. Key Words : Triangularization, Polynomial Matrices, Numerical Methods. y This work is part of the Barrande Project No. 97/005-97/026. It was also supported by the Grant Agency of the Czech Republic under contract No. 102/97/0861, by the Ministry of Education of the Czech Republic under contract No. VS97/034 and by the French Ministry of Education and Research under contract No. 10-INSA-96. z corresponding author. E-mail: henrion@laas.fr. FAX: (33 5) 61 33 69 69. 1 Introduction A com..