On exact rate of convergence of row sequences of multipoint Hermite-Padé approximants

• Autorzy: Bosuwan Nattapong

Identyfikatory

DOI

10.1515/dema-2023-0140

• Języki publikacji: EN

Abstrakty

EN

In this article, we analyze a rate of attraction of poles of an approximated function to poles of incomplete multipoint Padé approximants and use it to derive a sharp bound on the geometric rate of convergence of multipoint Hermite-Padé approximants to a vector of approximated functions in the Montessus de Ballore theorem when a table of interpolation points is Newtonian.

Słowa kluczowe

EN

Montessus de Ballore’s theorem; multipoint Padé approximation; Hermite-Padé approximation; simultaneous approximation; rate of convergence

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2024
• Tom: Vol. 57, nr 1
• Strony: art. no. 20230140
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Bosuwan Nattapong

• Department of Mathematics, Faculty of Science, Mahidol University, Rama VI Road, Ratchathewi District, Bangkok 10400, Thailand
• Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Bibliografia

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• [3] A. A. Gonchar, On the convergence of generalized Padé approximants of meromorphic functions, Math. USSR Sb. 140 (1975), 564–577.
• [4] E. B. Saff, An extension of Montessus de Ballore’s theorem on the convergence of interpolating rational functions, J. Approx. Theory 6 (1972), 63–67.
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• [7] J. Cacoq, B. de la Calle Ysern, and G. López Lagomasino, Incomplete Padé approximation and convergence of row sequences of Hermite-Padé approximants, J. Approx. Theory 170 (2013), 59–77.
• [8] J. Cacoq, B. de la Calle Ysern, and G. López Lagomasino, Direct and inverse results on row sequences of Hermite-Padé approximation, Constr. Approx. 38 (2013), 133–160.
• [9] C. Hermite, Sur la fonction exponentielle, C. R. Acad. Sci. Paris 77 (1873), 18–24, 74–79, 226–233, 285–293.
• [10] P. R. Graves-Morris and E. B. Saff, A de Montessus theorem for vector valued rational interpolants, in: P. R. Graves-Morris, E. B. Saff, and R. S. Varga (Eds), Rational Approximation and Interpolation, Springer, Germany, 1984, pp. 227–242.
• [11] G. López Lagomasino and Y. Zaldivar Gerpe, Inverse results on row sequences of Hermite-Padé approximation, Proc. Steklov Inst. Math. 298 (2017), 152–169.
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• [13] N. Bosuwan and G. López Lagomasino, Determining system poles using row sequences of orthogonal Hermite-Padé approximants, J. Approx. Theory 231 (2018), 15–40.
• [14] N. Bosuwan and G. López Lagomasino, Direct and inverse results on row sequences of simultaneous Padé-Faber approximants, Mediterr. J. Math. 16 (2019), 36, DOI: https://doi.org/10.1007/s00009-019-1307-0.
• [15] N. Bosuwan, Convergence of row sequences of simultaneous Padé-orthogonal approximants, Comput. Methods Funct. Theory 17 (2017), 525–556.
• [16] N. Bosuwan, G. López Lagomasino, and Y. Zaldivar Gerpe, Direct and inverse results for multipoint Hermite-Padé approximants, Anal. Math. Phys. 9 (2019), 761–779.
• [17] J. L. Walsh, Interpolation and Approximation by Rational Functions in the Complex Domain, American Mathematical Society, Providence, 1969.
• [18] A. A. Gonchar and L. D. Grigorjan, On estimates of the norm of the holomorphic component of a meromorphic function, Sb. Math. 28 (1976), 571–575.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).