Revisiting Some Pal Type Birkhoff Interpolation Problems

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Authors

  • A. K. Pathak
     ,IN
  • Poornima Tiwari
     ,IN

DOI:

https://doi.org/10.18311/jims/2019/22575

Keywords:

Lacunary Interpolation, Non-uniformly Distributed Nodes, Pal Type Birkhoff Interpolation, Regularity, Roots of Unity

Abstract

In this paper we revisit Pal type Birkhoff interpolation for the sets consisting of zeros of polynomials with complex coefficients with two or more additional nodes at value nodes. We also evaluate regularity of (0, 2) Pal type Birkhoff interpolation on the zeros of the polynomials obtained by applying mobius transform to the zeros of roots of unity with one additional complex node at value nodes.

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Published

2018-12-12

How to Cite

Pathak, A. K., & Tiwari, P. (2018). Revisiting Some Pal Type Birkhoff Interpolation Problems. The Journal of the Indian Mathematical Society, 86(1-2), 118–125. https://doi.org/10.18311/jims/2019/22575

Issue

Volume 86, Issue 1-2, January-June 2019

Section

Articles

License

Copyright (c) 2018 A. K. Pathak, Poornima Tiwari

Creative Commons License

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

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References

L. G. Pal, A new modification of the Hermite-Fejer interpolation, Anal. Math., 1 (1975), 197−205.

O. Kis, Notes on interpolation, Acta. Math. Acad. Sci. Hungar., 11 (1960) 49−64. (In Russian)

G. G. Lorentz, S. D. Riemschneider and K. Jetter, Birkhoff interpolation, Addison-Wesley, Mass., (1983).

W. Chen and A. Sharma, Lacunary interpolation on some non-uniformly distributed nodes on the unit circle, Annales Univ. Sci., Budapest., (Sectio Computatorica) 16 (1996), 69−82.

M. G. de Bruin and A. Sharma, Birkhoff interpolation on perturbed roots of unity on the unit circle, J. Nat. Acad. Math. India, 11 (1997), 83−87.

M. G. de Bruin, A. Sharma and J. Szabados, Birkhoff-type interpolation on perturbed roots of unity, in: Approximation Theory in Memory of A. K. Varma, N. K. Govil, R. N. Mohapatra, Z. Nashed, A. Sharma and J. Szabados (Eds.), Marcel Dekker, New York, (1998), 167−179.

M. A. Bokhari, H. P. Dikshit and A. Sharma, Birkhoff interpolation on some perturbed roots of unity: revisited, Numer. Algorithms, 25 (2000) 47−62.

H. P. Dikshit, Birkhoff interpolation on some perturbed roots of unity, Nonlinear Analysis Forum, 6 (2001), 97−102.

H. P. Dikshit, Pal-type interpolation on non-uniformly distributed nodes on the unit circle, Journal of Computational and Applied Mathematics, 155 (2003), 253−261.

M. G. de Bruin and H. P. Dikshit, Pal-type Birkhoff interpolation on nonuniformly distributed points, Numerical Algorithm, 40 (2005), 1−16.

M. G. de Bruin, (0,m) Pal-type interpolation on the mobius transform of roots of Unity, Journal of Computational and Applied Mathematics, 178 (2005), 147−153.

A. K. Pathak, A Birkhoff interpolation problem on unit circle in the complex plane, J. Indian Math. Soc., 73 (2006), 227−233.

R. Brueck, Lagrange interpolation in non-uniformly distributed nodes on the unit circle, Analysis 16 (1996), 273−282.

A. Mandloi and A. K. Pathak, (0,2) Pal-type interpolation on a circle in the complex plane involving mobius transform, Numer. Algorithms, 47 (2008), 181−190.

Geeta Modi, Anil Kumar Pathak and Anita Mandloi, Some cases of Pal-type birkhoff interpolation on zeros of polynomials with complex coefficients, Rocky Mountain Journal, 42 (2012), 711−727.