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Radau quadrature for a rational almost quasi-Hermite-Fej{\'e}r-type interpolation

Laxmi Rathour|Vishnu Narayan Mishra|Shrawan Kumar|Neha Mathur|Pankaj Mathur
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2022.03|한국수학논문집 (Korean Journal of Mathematics)|제30권 제1호|pp. 43-51

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참고문헌

키워드

Almost Quasi-Hermite-Fej{'e}r-type interpolationRadau-type quadraturerational spaceprescribed polesChebyshev-Markov fractions
주제분류수학

초록

The aim of this paper is to obtain a Radau type quadrature formula for a rational interpolation process satisfying the almost quasi Hermite Fej\'er interpolatory conditions on the zeros of Chebyshev Markov sine fraction on $[-1, 1)$.

Abstract

The aim of this paper is to obtain a Radau type quadrature formula for a rational interpolation process satisfying the almost quasi Hermite Fej\'er interpolatory conditions on the zeros of Chebyshev Markov sine fraction on $[-1, 1)$.

참고문헌 (13)

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  3. A. L. Lukashov, "Inequalities for the derivatives of rational functions on several intervals", Izv. Math, 68(3), pp.543~565 (2004)
  4. A. A. Markov, "Izbrannye trudy, Teoriya cisel. Teoriya veroyatnostei, Izdat" (1951), Akad. Nauk SSSR
  5. G. Min, "Lobatto-type quadrature formula in rational spaces", J. Comput. Appl. Math, 94(1), pp.1~12 (1998)
  6. Y. Rouba, "Rational quasi-Hermite-Fej´er-type interpolation and Lobatto-type quadrature formula with Chebyshev-Markov nodes", Jaen J. Approx, 7(2), pp.291~308 (2015)
  7. E. A. Rovba, "Interpolation rational operators of Fej´er and de la Valle-Poussin type", Mat. Zametki, 53(2), pp.195~200 (1993)[DOI]
  8. E. A. Rouba, "Interpoljacija i rjady Furie v ratsionalnoj approksimatsii", GrSU
  9. Y. A. Rouba, "Rational interpolation in the zeros of Chebyshev-Markov sine-fractions", Dokl. Nats. Akad. Nauk Belarusi, 52(5), pp.11~15 (2008)[DOI]
  10. V. N. Rusak, "Interpolation by rational functions with fixed poles", Dokl. Akad. Nauk BSSR, 6, pp.548~550 (1962)[DOI]
  11. V. N. Rusak, "On approximations by rational fractions", Dokl. Akad. Nauk BSSR, 8, pp.432~435 (1964)[DOI]
  12. A. H. Turecki, "Teorija interpolirovanija v zadachakh" (1968), Izdat “Vyssh. Skola”
  13. J. Van Deun, "Electrostatics and ghost poles in near best fixed pole rational interpolation", Electron. Trans. Numer. Anal, 26, pp.439~452 (2007)

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