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On certain sequences of least squares approximants

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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A sequence of certain rational functions is determined where each member solves an ℓ2-minimisation problem on a “large” set of roots of unity. The sequence is compared with another sequence of L2-rational approximants. Our main result extends a result of Rivlin on Walsh type equiconvergence.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 3 , June 1988 , pp. 415 - 422
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Rivlin, T.J., ‘On Walsh Equiconvergence’, J. Approz. Theory 36 (1982), 334–345.CrossRefGoogle Scholar
[2]Saff, E.B. and Sharma, A., ‘On equiconvergence of certain sequence of rational Interpolants’, Rational Approzimation and Interpolation Lecture Notes in Math 1105 (Springer, 1984).Google Scholar
[3]Walsh, J.L., ‘Interpolation and Approximation by Rational Functions in the complex Domain’, Colloq. Publ. 5th ed., Amer. Math. Soc. (1969).Google Scholar