Fraction-Free Computation of Matrix Rational Interpolants and Matrix GCDs

Bernhard Beckermann, George Labahn
2000 SIAM Journal on Matrix Analysis and Applications  
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 Pad e approximants, Newton-Pad e, Pad e-Hermite, simultaneous Pad e approximants and more generally M-Pad e approximants along with their matrix generalizations. The algorithms are fast and compute all solutions to a given problem. Solutions for all (possibly singular) subproblems along o diagonal paths in a solution table are
more » ... so computed by stepping around singular blocks on some path corresponding to \closest" regular interpolation problems. The algorithms are suitable for computation in exact arithmetic domains where growth of coe cients in intermediate computations are a central concern. This coe cient growth is avoided by using fraction-free methods. At the same time the methods are fast in the sense that they are at least an order of magnitude faster than existing fraction-free methods for the corresponding problems. The methods make use of linear systems having a special striped Krylov structure.
doi:10.1137/s0895479897326912 fatcat:jwa6tvzvrjdiva75mor64ryyai