A new algorithm for computing certified numerical approximations of the roots of a zero-dimensional system

Stef Graillat (1) , Philippe Trébuchet (2)

1 PEQUAN - Performance et Qualité des Algorithmes Numériques
2 APR - Algorithmes, Programmes et Résolution

This paper provides a new method for computing numerical approximations of the roots of a zero-dimensional system. It works on general systems, even those with multiple roots, and avoids any arbitrary choice of linear combination of the multiplication operators. It works by computing eigenvectors (or a basis of the full invariant subspaces). The sparsity/structure of the multiplication operators by one variable can also be taken into account.

Domaines: Informatique [cs]

Stef Graillat, Philippe Trébuchet. A new algorithm for computing certified numerical approximations of the roots of a zero-dimensional system. ISSAC'09 - the 2009 international symposium on Symbolic and algebraic computation, Jul 2009, Seoul, South Korea. pp.167-173, ⟨10.1145/1576702.1576727⟩. ⟨hal-01294713⟩