Geodesic
The Jacobi--Perron algorithm and simultaneous approximation of functions
Sbornik. Mathematics, Tome 42 (1982) no. 2, pp. 287-296

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A generalization of the Jacobi–Perron algorithm to the case of functions is considered. The rate is determined for the convergence (with respect to the coefficients of the Laurent series) of the generating rational functions to the functions that are being expanded in a continued fraction by means of this algorithm. A necessary and sufficient condition is given for a continued fraction to be broken off. Bibliography: 8 titles. 
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     author = {V. I. Parusnikov},
     title = {The {Jacobi--Perron} algorithm and simultaneous approximation of functions},
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V. I. Parusnikov. The Jacobi--Perron algorithm and simultaneous approximation of functions. Sbornik. Mathematics, Tome 42 (1982) no. 2, pp. 287-296. http://geodesic.mathdoc.fr/item/SM_1982_42_2_a4/