Efficient certication of numeric solutions to eigenproblems

Joris van der Hoeven (1) , Bernard Mourrain (2)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes

In this paper, we present an efficient algorithm for the certication of numeric solutions to eigenproblems. The algorithm relies on a mixture of ball arithmetic, a suitable Newton iteration, and clustering of eigenvalues that are close.

Mots clés: reliable computing; ball arithmetic; interval arithmetic; computable analysis

Domaines: Calcul formel [cs.SC]; Performance et fiabilité [cs.PF]; Logiciel mathématique [cs.MS]; Analyse numérique [math.NA]

Joris van der Hoeven, Bernard Mourrain. Efficient certication of numeric solutions to eigenproblems. MACIS 2017 - 7th International Conference on Mathematical Aspects of Computer and Information Sciences, Nov 2017, Vienna, Austria. pp.81--94, ⟨10.1007/978-3-319-72453-9_6⟩. ⟨hal-01579079⟩