References

  1. Dmytryshyn R.I. Associated branched continued fractions with two independent variables. Ukrainian Math. J. 2015, 66 (9), 1312-1323. doi: 10.1007/s11253-015-1011-6 (translation of Ukrain. Mat. Zh. 2014, 66 (9), 1175-1184. (in Ukrainian))
  2. Dmytryshyn R.I. Two-dimensional generalization of the Rutishauser $qd$-algorithm. J. Math. Sci. 2015, 208 (3), 301-309. doi: 10.1007/s10958-015-2447-9 (translation of Mat. Met. Fiz.-Mekh. Polya 2013, 56 (4), 33-39. (in Ukrainian))
  3. Dmytryshyn R.I. Regular two-dimensional $C$-fraction with independent variables for double power series. Bukovinskij Mat. Zh. 2013, 1 (1-2), 55-57. (in Ukrainian)
  4. Dmytryshyn R.I. The two-dimensional $g$-fraction with independent variables for double power series. J. Approx. Theory. 2012, 164 (12), 1520-1539. doi: 10.1016/j.jat.2012.09.002
  5. Dmytryshyn R.I. The multidimensional generalization of Bauer's $g$-algorithm. Carpathian Math. Publ. 2012, 4 (2), 247-260. (in Ukrainian)
  6. Kuchminska Ch.Yo. Two-Dimensional Continued Fractions. Pidstryhach Institute of Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, 2010. (in Ukrainian)
  7. Hoyenko N.P. Correspondence principle and convergence of sequences of analytic functions of several variables. Math. Bull. Shevchenko Sci. Soc. 2007, 4, 42-48. (in Ukrainian)
  8. Dmytryshyn R.I. The multidimensional generalization of $g$-fractions and their application. J. Comput. Appl. Math. 2004, 164-165, 265-284. doi: 10.1016/S0377-0427(03)00642-3
  9. Baran O.E., Bodnar D.I. The expansion of multiple power series into multidimensional $C$-fraction with independent variables. Volynskij Mat. Visn. 1999, 6, 15-20. (in Ukrainian)
  10. Bodnar D.I. Multidimensional $C$-fractions. J. Math. Sci. 1998, 90 (5), 2352-2359. doi: 10.1007/BF02433965 (translation of Mat. Met. Fiz.-Mekh. Polya 1996, 39 (3), 39-66. (in Ukrainian))
  11. Lorentzen L., Waadeland H. Continued Fractions with Applications. In: Studies in Computational Mathematics, 3. North-Holland, Amsterdam, London, New-York, Tokyo, 1992.
  12. Bodnar D.I. Corresponding branched continued fractions with linear partial numerators for double power series. Ukrain. Mat. Zh. 1991, 43 (4), 474-482. (in Russian)
  13. Cuyt A., Verdonk B. A review of branched continued fraction theory for the construction of multivariate rational approximations. Appl. Numer. Math. 1988, 4, 263-271. doi: 10.1016/0168-9274(83)90006-5
  14. Siemaszko W. Branched continued fractions for double power series. J. Comput. Appl. Math. 1980, 6 (2), 121-125. doi: 10.1016/0771-050X(80)90005-4
  15. Jones W.B., Thron W.J. Continued Fractions: Analytic Theory and Applications. In: Encyclopedia of Mathematics and its Applications, 11. Addison-Wesley, London, Amsterdam, Don Mills, Ontario, Sydney, Tokyo, 1980.
  16. Murphy J.F., O'Donohoe M.R. A two-variable generalisation of the Stieltjes-type continued fractions. J. Comput. Appl. Math. 1978, 4 (3), 181-190. doi: 10.1016/0771-050X(78)90002-5