Matrix Transformations and Disk of Convergence in Interpolation Processes

Chikkanna R. Selvaraj and Suguna Selvaraj

International Journal of Mathematics and Mathematical Sciences, 2008, vol. 2008, 1-11

Abstract:

Let ð ´ ð œŒ denote the set of functions analytic in | 𠑧 | < 𠜌 but not on | 𠑧 | = 𠜌 ( 1 < 𠜌 < ∞ ) . Walsh proved that the difference of the Lagrange polynomial interpolant of ð ‘“ ( 𠑧 ) ∈ ð ´ ð œŒ and the partial sum of the Taylor polynomial of ð ‘“ converges to zero on a larger set than the domain of definition of ð ‘“ . In 1980, Cavaretta et al. have studied the extension of Lagrange interpolation, Hermite interpolation, and Hermite-Birkhoff interpolation processes in a similar manner. In this paper, we apply a certain matrix transformation on the sequences of operators given in the above-mentioned interpolation processes to prove the convergence in larger disks.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:905635

DOI: 10.1155/2008/905635

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