Radau Quadrature for an Almost Quasi-Hermite-Fejer-Type Interpolation in Rational Spaces

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Shrawan Kumar
Neha Mathur
Vishnu Narayan Mishra
Pankaj Mathur

Abstract

In this paper, we have studied an almost quasi Hermite-Fejer-type interpolation in rational spaces. A Radau type quadrature formula has also been obtained for the same.

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References

  1. P. Borwein and T. Erdelyi, Polynomials and Polynomial Inequalities, Graduate Texts in Mathematics 161, Springer-Verlag, New York (1995).
  2. A. L. Lukashov, Inequalities for the derivatives of rational functions on several intervals, Izv. Math. 68(3) (2004), 543-565.
  3. A. A. Markov(1951), Izbrannye trudy, Teoriya cisel. Teoriya veroyatnostei, Izdat. Akad. Nauk SSSR, Leningrad.
  4. G. Min, Lobatto-type quadrature formula in rational spaces, J. Comput. Appl. Math. 94(1) (1998), 1-12.
  5. Y. Rouba, K. Smatrytski and Y. Dirvuk, Rational quasi-Hermite-Fejer-type interpolation and Lobatto-type quadrature formula with Chebyshev-Markov nodes, Jaen J. Approx. 7(2) (2015), 291-308
  6. E. A. Rovba, Interpolation rational operators of Fej ´er and de la Valle-Poussin type, Mat. Zametki., 53(2) (1993), 114-121 (in Russian, English translation: Math. Notes. 53 (1993), 195-200.
  7. E. A. Rouba, Interpoljacija i rjady Furie v ratsionalnoj approksimatsii, GrSU, Grodno. (2001).
  8. 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 (in Russian).
  9. V. N. Rusak, Interpolation by rational functions with fixed poles, Dokl. Akad. Nauk BSSR 6 (1962), 548-550 (in Russian).
  10. V. N. Rusak, On approximations by rational fractions, Dokl. Akad. Nauk BSSR 8 (1964), 432-435 (in Russian).
  11. A. H. Turecki, Teorija interpolirovanija v zadachakh, Izdat “Vyssh. Skola”, Minsk. (1968).
  12. J. Van Deun, Electrostatics and ghost poles in near best fixed pole rational interpolation, Electron. Trans. Numer. Anal. 26 (2007), 439-452