TY  - JOUR
A1  - Rössner, Carsten
A1  - Schnorr, Claus Peter
T1  - An optimal, stable continued fraction algorithm for arbitrary dimension
N2  - 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.
KW  - continued fraction algorithm
KW  - integer relation
KW  - simultaneous diophantine approximations
KW  - Dirichlet bound
KW  - floating point arithmetic
Y1  - 2005
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/4237
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30-12463
UR  - http://www.mi.informatik.uni-frankfurt.de/research/papers.html
N1  - Postprint, auch in: 5th IPCO Conference on Integer Programming and Combinatorial Optimization.Springer LNCS 1084, 31 - 43, 1996 , s.a. ECCC Report TR96-020
ER  -