Multidimensional continued fraction and rational approximation

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dc.creatorDai, Zongduo
dc.creatorWang, Kunpeng
dc.creatorYe, Dingfeng
dc.date2004-01-14
dc.date.accessioned2026-07-07T05:04:31Z
dc.date.available2026-07-07T05:04:31Z
dc.descriptionThe classical continued fraction is generalized for studying the rational approximation problem on multi-formal Laurent series in this paper, the construction is called m-continued fraction. It is proved that the approximants of an m-continued fraction converge to a multi-formal Laurent series, and are best rational approximations to it; conversely for any multi-formal Laurent series an algorithm called m-CF transform is introduced to obtain its m-continued fraction expansions; moreover, strict m-continued fractions, which are m-continued fractions imposed with some additional conditions, and multi-formal Laurent series are in 1-1 correspondence. It is shown that m-continued fractions can be used to study the multi-sequence synthesis problem.
dc.description18 pages, AMSLaTeX
dc.identifierhttps://arxiv.org/abs/math/0401141
dc.identifierhttp://arxiv.org/abs/math/0401141
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69836
dc.subjectNumber Theory
dc.subject11J70, 11Y65
dc.titleMultidimensional continued fraction and rational approximation
dc.typetext

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