Lattice basis reduction algorithms and multi-dimensional continued fractions

In this paper we develop a new multi-dimensional continued fraction algorithm and three known multi-dimensional continued fraction algorithms from the lattice basis reduction multisequence synthesis (LBRMS) algorithm with respect to the different choice of a parameter and so a continued fraction expansion is associated with a basis transformation. The new algorithm is similar to Daiʹs continued fraction algorithm [Z.D. Dai, K.P. Wang, D.F. Ye, m-Continued fraction algorithm on multi-Laurent series, Acta Arith. (2006) 1–21] but improves the latter effectively.