ESTIMATION OF THE LEBESGUE CONSTANT FOR THE RATIONAL LAGRANGE INTERPOLATION PROCESSES THROUGH THE CHEBYSHEV – MARKOV NODES

Y. A. Rovba; Y. V. Dirvuk

doi:undefined

ESTIMATION OF THE LEBESGUE CONSTANT FOR THE RATIONAL LAGRANGE INTERPOLATION PROCESSES THROUGH THE CHEBYSHEV – MARKOV NODES

Y. A. Rovba, Y. V. Dirvuk

Full Text:

PDF (Rus) |

Generate QR code

Abstract

This article considers the Lagrange interpolation processes, in which as interpolation nodes the zeros of the first-kind rational Chebyshev – Markov functions are chosen. The Lebesgue constant in the case of real poles is estimated.

Keywords

Lagrange interpolation process, rational Chebyshev – Markov functions, estimate of the Lebesgue constant

References

1. Privalov, A. A. Teoriya interpolirovaniya funktsii: v 2 kn. / A. A. Privalov. - Saratov: Izd-vo Sarat. un-ta, 1990. - Kn. 1. - 1990. - S. 1-229; kn. 2. - 1990. - S. 231-422.

2. Bernshtein, S. N. Ob ogranichenii znachenii mnogochlena Pn(x) stepeni n na vsem otrezke po ego znacheniyam v n + 1 tochkakh otrezka / S. N. Bernshtein // Sobr. soch.: v 4 t. - M., 1952. - T. 2. - S. 107-126.

3. Ivanov, V. V. Nekotorye novye rezul'taty v teorii approksimatsii / V. V. Ivanov // Vychislitel'naya matematika. Kiev: Izd-vo Kiev. un-ta, 1966. - S. 30-36.

4. Dzjadyk, V. K. On asymptotics and estimates for the uniform norms of the Lagrange interpolation polynomials corresponding to the Chebyshev nodal points / V. K. Dzjadyk, V. V. Ivanov // Anal. Math. - 1983. - Vol. 9. - P. 85-97.

5. Cheney, E. W. A note on some Lebesgue constants / E. W. Cheney, T. J. Rivlin // Center for numerical analysis (University of Texas at Austin), February 1975, CAN-98. - P. 1-7.

6. Rusak, V. N. Ob interpolirovanii ratsional'nymi funktsiyami s fiksirovannymi polyusami / V. N. Rusak // Dokl. Akad. nauk BSSR. - 1962. - T. 4, № 9. - S. 548-550.

7. Borwein, P. Zeros of Chebyshev polynomials in Markov systems / P. Borwein // J. Approx. Theory. - 1990. - Vol. 63. - P. 56-64.

8. Min, G. Lobbatto-type quadrature formuala in rational space / G. Min // J. Comput. and Appl. Math. - 1998. - N 94. - P. 1-12.

9. Starovoitov, A. P. O ratsional'noi interpolyatsii s fiksirovannymi polyusami / A. P. Starovoitov // Izv. Akakd. nauk BSSR. Ser. fiz.-mat. nauk. - 1983. - № 6. - S. 105-106.

10. Lukashov, A. L. Ratsional'nye interpolyatsionnye protsessy na neskol'kikh otrezkakh / A. L. Lukashov // Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika. - 2005. - T. 5 (1). - S. 34-48.

11. Rovba, E. A. Ratsional'noe interpolirovanie v nulyakh sinus-drobei Chebysheva - Markova / E. A. Rovba, K. A. Smotritskii // Dokl. Nats. akad. Belarusi. - 2008. - T. 52, № 5. - S. 11-15.

12. Smotritskii, K. A. O normakh interpolyatsionnykh protsessov s fiksirovannymi uzlami / K. A Smotritskii, E. V. Dirvuk // Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika.- 2014. - T. 14, vyp. 4 (2). - S. 590-595.

This work is licensed under a Creative Commons Attribution 4.0 License.

ISSN 1561-2430 (Print)
ISSN 2524-2415 (Online)

Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series

ESTIMATION OF THE LEBESGUE CONSTANT FOR THE RATIONAL LAGRANGE INTERPOLATION PROCESSES THROUGH THE CHEBYSHEV – MARKOV NODES

Full Text:

Abstract

Keywords

About the Authors

References

Review

Username
Password
	Remember me

User

Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series

ESTIMATION OF THE LEBESGUE CONSTANT FOR THE RATIONAL LAGRANGE INTERPOLATION PROCESSES THROUGH THE CHEBYSHEV – MARKOV NODES

Full Text:

Abstract

Keywords

About the Authors

References

Review

Cookies policy