Selmer's Multiplicative Algorithm

J. Christopher Kops

doi:10.1515/integ.2011.080

Selmer's Multiplicative Algorithm

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

The behavior of the multiplicative acceleration of Selmer’s algorithm is widely unknown and no general result on convergence has been detected yet. Solely for its 2-dimensional, periodic expansions, there exist some results on convergence and approximation due to Fritz Schweiger. In this paper we show that periodic expansions of any dimension do in fact converge and that the coordinates of the limit points are rational functions of the largest eigenvalue of the periodicity matrix.

Original language	English
Pages (from-to)	1-20
Number of pages	20
Journal	Integers
Volume	12
DOIs	https://doi.org/10.1515/integ.2011.080
Publication status	Published - 2011
Externally published	Yes

Keywords

multidimensional continued fractions
Selmer
Periodic expansions

Access to Document

10.1515/integ.2011.080

Cite this

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KW - Selmer

KW - Periodic expansions

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