Geodesic
Simplex-module algorithm for expansion of algebraic numbers in multidimensional continued fractions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 32, Tome 449 (2016), pp. 130-167

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Simplex-module algorithm ($\mathcal{SM}$-algorithm) for expansion of algebraic numbers $\alpha=(\alpha_1,\ldots,\alpha_d)$ in multidimensional continued fractions is offered. The method is based on 1) minimal rational simplices $\mathbf s$, where $\alpha\in\mathbf s$, and 2) Pisot matrices $P_\alpha$ for which $\widehat \alpha=(\alpha_1,\ldots,\alpha_d,1)$ is eigenvector. A multi-dimensional generalization of the Lagrange theorem is proved. 
@article{ZNSL_2016_449_a6,
     author = {V. G. Zhuravlev},
     title = {Simplex-module algorithm for expansion of algebraic numbers in multidimensional continued fractions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {130--167},
     publisher = {mathdoc},
     volume = {449},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_449_a6/}
}
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V. G. Zhuravlev. Simplex-module algorithm for expansion of algebraic numbers in multidimensional continued fractions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 32, Tome 449 (2016), pp. 130-167. http://geodesic.mathdoc.fr/item/ZNSL_2016_449_a6/