A fraction free Matrix Berlekamp/Massey algorithm

A Fraction Free Matrix Berlekamp/Massey Algorithm*

We describe a fraction free version of the Matrix Berlekamp/Massey algorithm. The algorithm computes a minimal matrix generator of linearly generated square matrix sequences over an integral domain. The algorithm performs all operations in the integral domain, so all divisions performed are exact. For scalar sequences, the matrix algorithm specializes to a more efficient algorithm than the algo...

A matrix Euclidean algorithm and matrix continued fraction expansions

Matrix factoring by fraction-free reduction

We consider exact matrix decomposition by Gauss-Bareiss reduction. We investigate two aspects of the process: common row and column factors and the influence of pivoting strategies. We identify two types of common factors: systematic and statistical. Systematic factors depend on the process, while statistical factors depend on the specific data. We show that existing fraction-free QR (Gram–Schm...

Fraction-Free Computation of Matrix Rational Interpolants and Matrix GCDs

We present a new set of algorithms for computation of matrix rational interpolants and one-sided matrix greatest common divisors. Examples of these interpolants include Padé approximants, Newton–Padé, Hermite–Padé, and simultaneous Padé approximants, and more generally M-Padé approximants along with their matrix generalizations. The algorithms are fast and compute all solutions to a given probl...

Fraction-free Computation of Matrix Pad E Systems

We present a fraction-free approach to the computation of matrix Pad e systems. The method relies on determining a modiied Schur complement for the coeecient matrices of the linear systems of equations that are associated to matrix Pad e approximation problems. By using this modiied Schur complement for these matrices we are able to obtain a hybrid fraction-free algorithm for their computation....