Geodesic
The Jacobi–Perron algorithm and simultaneous approximation of functions
Sbornik. Mathematics, Tome 42 (1982) no. 2, pp. 287-296 
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/
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     author = {V. I. Parusnikov},
     title = {The {Jacobi{\textendash}Perron} algorithm and simultaneous approximation of functions},
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     volume = {42},
     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/SM_1982_42_2_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] O. Perron, Die Lehre von den Kettenbruchen, Teubner, Stuttgart, 1957 | MR | Zbl

[2] O. Perron, “Grundlagen fur eine Theorie des Jacobische Kettenbruchalgoritmus”, Math. Ann., 64 (1907), 1–76 | DOI | MR | Zbl

[3] M. G. de Bruin, “The interruption phenomenon for generalized continued fractions”, Bull. Austr. Math. Soc., 19:2 (1978), 245–272 | DOI | MR | Zbl

[4] M. G. de Bruin, “Convergence of generalized $C$-fractions”, J. Appr. Th., 24:3 (1978), 177–207 | DOI | MR | Zbl

[5] H. S. Wall, Analytic theory of continued fractions, New York, 1948 | MR

[6] A. Magnus, “Expansion of power series into $P$-fractions”, Math. Z., 80:3 (1969), 209–216 | MR

[7] J. Coates, “On the algebraic approximation of functions”, ser. A, Nederl. Akad. Wetensch., 69 (1966), 421–461 | MR | Zbl

[8] E. M. Nikishin, “O sistemakh markovskikh funktsii”, Vestnik MGU, matem., mekhan., 1979, no. 4, 60–63 | MR | Zbl