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
LIP6 - Laboratoire d'Informatique de Paris 6
2 APR - Algorithmes, Programmes et Résolution
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : 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.
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Conference papers
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https://hal.archives-ouvertes.fr/hal-01294713
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Submitted on : Tuesday, March 29, 2016 - 4:54:12 PM
Last modification on : Thursday, March 21, 2019 - 1:06:51 PM

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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⟩

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