18 citations · 27 across the 7 of their papers we have counts for
5 papers · 1 filter
Finding simultaneous Diophantine approximations with prescribed quality
Wieb Bosma, Ionica Smeets
We give an algorithm that finds a sequence of approximations with Dirichlet coefficients bounded by a constant only depending on the dimension. The algorithm uses the LLL-algorithm…
Approximation Results for alpha-Rosen Fractions
Cor Kraaikamp, Ionica Smeets
In this article we generalize Borel's classical approximation results for the regular continued fraction expansion to the alpha-Rosen fraction expansion, using a geometric method.…
Quilting natural extensions for alpha-Rosen Fractions
Cor Kraaikamp, Thomas A. Schmidt, Ionica Smeets
We give natural extensions for the alpha-Rosen continued fractions of Dajani et al. for a set of small alpha values by appropriately adding and deleting rectangles from the region…
Sharp bounds for symmetric and asymmetric Diophantine approximation
Cor Kraaikamp, Ionica Smeets
In 2004, J.C. Tong found bounds for the approximation quality of a regular continued fraction convergent of a rational number, expressed in bounds for both the previous and next ap…
Tong's spectrum for Rosen continued fractions
Cor Kraaikamp, Thomas A. Schmidt, Ionica Smeets
The Rosen fractions are an infinite set of continued fraction algorithms, each giving expansions of real numbers in terms of certain algebraic integers. For each, we give a best po…