Lattice basis reduction algorithms and multi-dimensional continued fractions (Q958608)

In [\textit{L. Wang} and \textit{Y. Zhu}, Sci. China, Ser. F 44, 321--328 (2001; Zbl 1125.94318) and \textit{L. Wang, Y. Zhu} and \textit{D. Pei} [IEEE Trans. Inf. Theory 50, 2905--2910 (2004; Zbl 1178.94181)] the author et al. proposed a lattice basis reduction algorithm for finding the joint minimal polynomial of a given (finite) \(m\)-fold multisequence, which is related to best simultaneous rational approximation of multiple Laurent series. Based on the previous papers the author develops a new lattice basis reduction algorithm. The resulting new multi-dimensional continued fraction algorithm is similar to the algorithm presented in \textit{Z. D. Dai, K. P. Wang} and \textit{D. F. Ye} [Acta Arith. 122, 1--16 (2006; Zbl 1146.11036)], but improves its performance.