Efficient certification of numeric solutions to eigenproblems

Joris van der Hoeven; Bernard Mourrain

doi:10.1007/978-3-319-72453-9_6

Efficient certification of numeric solutions to eigenproblems

Joris van der Hoeven
, Bernard Mourrain

INRIA

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper, we present an efficient algorithm for the certification 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.

Original language	English
Title of host publication	Mathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings
Editors	Ilias S. Kotsireas, Johannes Blomer, Dimitris E. Simos, Temur Kutsia
Publisher	Springer Verlag
Pages	81-94
Number of pages	14
ISBN (Print)	9783319724522
DOIs	https://doi.org/10.1007/978-3-319-72453-9_6
Publication status	Published - 1 Jan 2017
Event	7th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2017 - Vienna, Austria Duration: 15 Nov 2017 → 17 Nov 2017

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10693 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	7th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2017
Country/Territory	Austria
City	Vienna
Period	15/11/17 → 17/11/17

Keywords

Ball arithmetic
Computable analysis
Interval arithmetic
Reliable computing

Access to Document

10.1007/978-3-319-72453-9_6

Cite this

van der Hoeven, J., & Mourrain, B. (2017). Efficient certification of numeric solutions to eigenproblems. In I. S. Kotsireas, J. Blomer, D. E. Simos, & T. Kutsia (Eds.), Mathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings (pp. 81-94). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10693 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-72453-9_6

van der Hoeven, Joris ; Mourrain, Bernard. / Efficient certification of numeric solutions to eigenproblems. Mathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings. editor / Ilias S. Kotsireas ; Johannes Blomer ; Dimitris E. Simos ; Temur Kutsia. Springer Verlag, 2017. pp. 81-94 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Efficient certification of numeric solutions to eigenproblems",

abstract = "In this paper, we present an efficient algorithm for the certification 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.",

keywords = "Ball arithmetic, Computable analysis, Interval arithmetic, Reliable computing",

author = "\{van der Hoeven\}, Joris and Bernard Mourrain",

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doi = "10.1007/978-3-319-72453-9\_6",

language = "English",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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editor = "Kotsireas, \{Ilias S.\} and Johannes Blomer and Simos, \{Dimitris E.\} and Temur Kutsia",

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van der Hoeven, J & Mourrain, B 2017, Efficient certification of numeric solutions to eigenproblems. in IS Kotsireas, J Blomer, DE Simos & T Kutsia (eds), Mathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10693 LNCS, Springer Verlag, pp. 81-94, 7th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2017, Vienna, Austria, 15/11/17. https://doi.org/10.1007/978-3-319-72453-9_6

Efficient certification of numeric solutions to eigenproblems. / van der Hoeven, Joris; Mourrain, Bernard.
Mathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings. ed. / Ilias S. Kotsireas; Johannes Blomer; Dimitris E. Simos; Temur Kutsia. Springer Verlag, 2017. p. 81-94 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10693 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Efficient certification of numeric solutions to eigenproblems

AU - van der Hoeven, Joris

AU - Mourrain, Bernard

N1 - Publisher Copyright: © Springer International Publishing AG 2017.

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Y1 - 2017/1/1

N2 - In this paper, we present an efficient algorithm for the certification 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.

AB - In this paper, we present an efficient algorithm for the certification 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.

KW - Ball arithmetic

KW - Computable analysis

KW - Interval arithmetic

KW - Reliable computing

U2 - 10.1007/978-3-319-72453-9_6

DO - 10.1007/978-3-319-72453-9_6

M3 - Conference contribution

AN - SCOPUS:85039434114

SN - 9783319724522

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 81

EP - 94

BT - Mathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings

A2 - Kotsireas, Ilias S.

A2 - Blomer, Johannes

A2 - Simos, Dimitris E.

A2 - Kutsia, Temur

PB - Springer Verlag

T2 - 7th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2017

Y2 - 15 November 2017 through 17 November 2017

ER -

van der Hoeven J, Mourrain B. Efficient certification of numeric solutions to eigenproblems. In Kotsireas IS, Blomer J, Simos DE, Kutsia T, editors, Mathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings. Springer Verlag. 2017. p. 81-94. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-72453-9_6

Efficient certification of numeric solutions to eigenproblems

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