Efficient certication of numeric solutions to eigenproblems

Joris Van Der Hoeven 1 Bernard Mourrain 2
2 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
CRISAM - Inria Sophia Antipolis - Méditerranée , National and Kapodistrian University of Athens
Abstract : 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.
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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⟩

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