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RADAU QUADRATURE FOR A RATIONAL ALMOST QUASI-HERMITE-FEJÉR-TYPE INTERPOLATION

  • Received : 2021.05.29
  • Accepted : 2022.02.08
  • Published : 2022.03.30

Abstract

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

Keywords

References

  1. P. Borwein and T. Erdelyi, Polynomials and Polynomial Inequalities, Graduate Texts in Mathematics 161, Springer-Verlag, New York (1995).
  2. S. Kumar, N. Mathur, V. N. Mishra and P. Mathur, Radau Quadrature for an Almost Quasi-Hermite-Fejer-type interpolation in Rational Spaces, Int. J. Anal. Appl. 19 (2) (2021), 180-192.
  3. A. L. Lukashov, Inequalities for the derivatives of rational functions on several intervals, Izv. Math. 68 (3) (2004), 543-565. https://doi.org/10.1070/IM2004v068n03ABEH000488
  4. A. A. Markov, Izbrannye trudy, Teoriya cisel. Teoriya veroyatnostei, Izdat. Akad. Nauk SSSR, Leningrad (1951).
  5. G. Min, Lobatto-type quadrature formula in rational spaces, J. Comput. Appl. Math. 94 (1) (1998), 1-12. https://doi.org/10.1016/S0377-0427(98)00068-5
  6. Y. Rouba, K. Smatrytski and Y. Dirvuk, Rational quasi-Hermite-Fej'er-type interpolation and Lobatto-type quadrature formula with Chebyshev-Markov nodes, Jaen J. Approx. 7 (2) (2015), 291-308.
  7. E. A. Rovba, Interpolation rational operators of Fej'er and de la Valle-Poussin type, Mat. Zametki. 53 (2) (1993), 114-121 (English translation: Math. Notes. 53 (1993), 195-200).
  8. E. A. Rouba, Interpoljacija i rjady Furie v ratsionalnoj approksimatsii, GrSU, Grodno.
  9. Y. A. Rouba and K. A. Smatrytski, Rational interpolation in the zeros of Chebyshev-Markov sine-fractions, Dokl. Nats. Akad. Nauk Belarusi 52 (5) (2008), 11-15.
  10. V. N. Rusak, Interpolation by rational functions with fixed poles, Dokl. Akad. Nauk BSSR 6 (1962), 548-550.
  11. V. N. Rusak, On approximations by rational fractions, Dokl. Akad. Nauk BSSR 8 (1964), 432-435.
  12. A. H. Turecki, Teorija interpolirovanija v zadachakh, Izdat "Vyssh. Skola", Minsk (1968).
  13. J. Van Deun, Electrostatics and ghost poles in near best fixed pole rational interpolation, Electron. Trans. Numer. Anal. 26 (2007), 439-452.