An optimal, stable continued fraction algorithm for arbitrary dimension
We analyse a continued fraction algorithm (abbreviated CFA) for arbitrary dimension n showing that it produces simultaneous diophantine approximations which are up to the factor 2^((n+2)/4) best possible. Given a real vector x=(x_1,...,x_{n-1},1) in R^n this CFA generates a sequence of vectors (p_1^(k),...,p_{n-1}^(k),q^(k)) in Z^n, k=1,2,... with increasing integers |q^{(k)}| satisfying for i=1,...,n-1 | x_i - p_i^(k)/q^(k) | <= 2^((n+2)/4) sqrt(1+x_i^2) |q^(k)|^(1+1/(n-1)) By a theorem of Dirichlet this bound is best possible in that the exponent 1+1/(n-1) can in general not be increased.Download full text files
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| Author: | Carsten Rössner, Claus Peter Schnorr |
|---|---|
| URN: | urn:nbn:de:hebis:30-12463 |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 19.07.2005 |
| Year of first Publication: | 1996 |
| Publishing Institution: | Univ.-Bibliothek Frankfurt am Main |
| Tag: | Dirichlet bound ; continued fraction algorithm ; floating point arithmetic; integer relation ; simultaneous diophantine approximations |
| Source: | 5th IPCO Conference on Integer Programming and Combinatorial Optimization.Springer LNCS 1084, 31 - 43, 1996 , s.a. ECCC Report TR96-020 , http://www.mi.informatik.uni-frankfurt.de/research/papers.html |
| HeBIS PPN: | 224866249 |
| Institutes: | Mathematik |
| Informatik | |
| Dewey Decimal Classification: | 510 Mathematik |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Veröffentlichungsvertrag für Publikationen ohne Print on Demand |
