2004/01/14 by Zongduo Dai, Dai, Zongduo, Kunpeng Wang +3
Computer Science · Mathematics · #11J70 #11Y65 #Coding theory and cryptography #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Numerical Methods and Algorithms #math.NT #msc:11J70 #msc:11Y65
paper · pdf · doi:10.48550/arxiv.math/0401141
18 pages, AMSLaTeX
arxiv created 2004/01/14 · openalex publication_date 2004/01/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The 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.