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Perturbation of nodes and poles in certain rational interpolants

Published online by Cambridge University Press:  17 April 2009

M.A. Bokhari
M.A. Bokhari
Affiliation:
Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan
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Abstract

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Recently, E.B. Saff and A. Sharma proved a result on Walsh's type equiconvergence for certain sequences of rational interpolants having uniformly distributed poles and nodes of interpolation. Here we examine the sensitivity of this result to a slight perturbation of the poles and nodes. Some problems related to our work are also formulated.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 2 , October 1987 , pp. 177 - 185
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Bokhari, M.A., Equiconvergence of some interpolatory and best approximating processes. (Ph.D. Thesis, University of Alberta, 1986).Google Scholar
[2]Saff, E.B. and Sharma, A., “On equiconvergence of certain sequences of rational interpolants”, Proc. Rational approximations and interpolation (Lecture Notes in Math. 1105. Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1984) 256–271.CrossRefGoogle Scholar
[3]Szabados, J., and Varga, R.S., “On the overconvergence of complex interpolating polynomials”, J. Approx. Theory 36 (1982), 346–363.CrossRefGoogle Scholar
[4]Walsh, J.L., Interpolation and Approximation by rational functions in the complex domain. 5th ed., (Amer. Math. Soc. Colloq. Publ. 20, Providence, R.I., 1969).Google Scholar