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Mat. Sb. (N.S.), 1981, Volume 114(156), Number 2, Pages 322–333 (Mi msb2327)  

This article is cited in 22 scientific papers (total in 22 papers)

The Jacobi–Perron algorithm and simultaneous approximation of functions

V. I. Parusnikov


Abstract: 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.

Full text: PDF file (895 kB)
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English version:
Mathematics of the USSR-Sbornik, 1982, 42:2, 287–296

Bibliographic databases:

UDC: 517.5
MSC: 30B70, 40A15, 40A25
Received: 28.02.1980

Citation: V. I. Parusnikov, “The Jacobi–Perron algorithm and simultaneous approximation of functions”, Mat. Sb. (N.S.), 114(156):2 (1981), 322–333; Math. USSR-Sb., 42:2 (1982), 287–296

Citation in format AMSBIB
\Bibitem{Par81}
\by V.~I.~Parusnikov
\paper The Jacobi--Perron algorithm and simultaneous approximation of functions
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 114(156)
\issue 2
\pages 322--333
\mathnet{http://mi.mathnet.ru/msb2327}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=609293}
\zmath{https://zbmath.org/?q=an:0484.30005|0461.30003}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 42
\issue 2
\pages 287--296
\crossref{https://doi.org/10.1070/SM1982v042n02ABEH002254}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. M. Nikishin, “On simultaneous Padé approximants”, Math. USSR-Sb., 41:4 (1982), 409–425  mathnet  crossref  mathscinet  zmath
    2. Parusnikov V., “Weakly Perfect Systems of Functions and Multidimensional Continued Fractions”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1984, no. 2, 13–17  mathscinet  zmath  isi
    3. G Baker, “Convergence theorems for rows of differential and algebraic Hermite-Padé approximations”, Journal of Computational and Applied Mathematics, 18:1 (1987), 29  crossref
    4. Aptekarev A. Kalyagin V., “Analytic Properties of Two-Dimensional Continued P-Fraction Expansions with Periodical Coefficients and their Simultaneous Pade-Hermite Approximants”, Lect. Notes Math., 1237 (1987), 145–160  crossref  mathscinet  zmath  isi
    5. Parusnikov V., “On the Convergence of the Multidimensional Limit-Periodic Continued Fractions”, Lect. Notes Math., 1237 (1987), 217–227  crossref  mathscinet  zmath  isi
    6. Tamura J., “A Class of Transcendental-Numbers with Explicit G-Adic Expansion and the Jacobi-Perron Algorithm”, Acta Arith., 61:1 (1992), 51–67  mathscinet  zmath  isi
    7. V. A. Kalyagin, “Hermite–Padé approximants and spectral analysis of nonsymmetric operators”, Russian Acad. Sci. Sb. Math., 82:1 (1995), 199–216  mathnet  crossref  mathscinet  zmath  isi
    8. Yu. V. Nesterenko, “Hermite–Padé approximants of generalized hypergeometric functions”, Russian Acad. Sci. Sb. Math., 83:1 (1995), 189–219  mathnet  crossref  mathscinet  zmath  isi
    9. V. Kaliaguine, “The operator moment problem, vector continued fractions and an explicit form of the Favard theorem for vector orthogonal polynomials”, Journal of Computational and Applied Mathematics, 65:1-3 (1995), 181  crossref
    10. V. N. Sorokin, “Completely integrable nonlinear dynamical systems of the Langmuir chains type”, Math. Notes, 62:4 (1997), 488–500  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. Vladimir N. Sorokin, Jeannette Van Iseghem, “Matrix Continued Fractions”, Journal of Approximation Theory, 96:2 (1999), 237  crossref
    12. Sorokin, V, “Matrix Hermite-Pade problem and dynamical systems”, Journal of Computational and Applied Mathematics, 122:1–2 (2000), 275  crossref  isi  elib
    13. Van Iseghem J., “Matrix Continued Fraction for the Resolvent Function of the Band Operator”, Acta Appl. Math., 61:1-3 (2000), 351–365  crossref  mathscinet  isi
    14. Aptekarev A., Kaliaguine V., Van Iseghem J., “The Genetic Sums' Representation for the Moments of a System of Stieltjes Functions and its Application”, Constr. Approx., 16:4 (2000), 487–524  crossref  mathscinet  zmath  isi
    15. W.V.an Assche, Els Coussement, “Some classical multiple orthogonal polynomials”, Journal of Computational and Applied Mathematics, 127:1-2 (2001), 317  crossref
    16. M.Castro Smirnova, “Convergence Conditions for Vector Stieltjes Continued Fractions”, Journal of Approximation Theory, 115:1 (2002), 100  crossref
    17. Van Iseghem J., “Vector Stieltjes Continued Fraction and Vector Qd Algorithm”, Numer. Algorithms, 33:1-4 (2003), 485–498  crossref  mathscinet  zmath  adsnasa  isi
    18. V. I. Parusnikov, “A Generalization of Pincherle's Theorem to $k$-Term Recursion Relations”, Math. Notes, 78:6 (2005), 827–840  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    19. A. I. Aptekarev, D. N. Tulyakov, “Glavnyi chlen asimptotiki reshenii chetyrekhchlennykh rekursii”, Preprinty IPM im. M. V. Keldysha, 2013, 001, 20 pp.  mathnet
    20. A. I. Aptekarev, S. A. Denisov, M. L. Yattselev, “Vpolne integriruemye na $\mathbb{Z}_+^d$ potentsialy dlya elektromagnitnogo operatora Shredingera: luchevye asimptotiki i zadacha rasseyaniya”, Preprinty IPM im. M. V. Keldysha, 2015, 088, 20 pp.  mathnet
    21. Mano T., Tsuda T., “Hermite–Padé approximation, isomonodromic deformation and hypergeometric integral”, Math. Z., 285:1-2 (2017), 397–431  crossref  mathscinet  zmath  isi  scopus
    22. D. Barrios Rolanía, J. S. Geronimo, G. López Lagomasino, “High-order recurrence relations, Hermite-Padé approximation and Nikishin systems”, Sb. Math., 209:3 (2018), 385–420  mathnet  crossref  crossref  adsnasa  isi  elib
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