TY - JOUR
A1 - RÃ¶ssner, 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 - 1996
UR - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/4237
UR - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:hebis:30-12463
ER -