Matrix transformations and disk of convergence in interpolation processes

Chikkanna R. Selvaraj, Suguna Selvaraj

Research output: Contribution to journalArticle

Abstract

Let Aρ denote the set of functions analytic in z < ρ but not on z = ρ (1 < ρ < ∞). Walsh proved that the difference of the Lagrange polynomial interpolant of f(z) ∈ Aρ and the partial sum of the Taylor polynomial of f converges to zero on a larger set than the domain of definition of f. 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.

Original languageEnglish (US)
Article number905635
JournalInternational Journal of Mathematics and Mathematical Sciences
Volume2008
DOIs
StatePublished - Dec 30 2008

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Matrix Transformation
Hermite Interpolation
Interpolate
Birkhoff Interpolation
Lagrange's polynomial
Taylor Polynomial
Lagrange Interpolation
Interpolants
Partial Sums
Large Set
Analytic function
Denote
Converge
Zero
Operator

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

Cite this

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Matrix transformations and disk of convergence in interpolation processes. / Selvaraj, Chikkanna R.; Selvaraj, Suguna.

In: International Journal of Mathematics and Mathematical Sciences, Vol. 2008, 905635, 30.12.2008.

Research output: Contribution to journalArticle

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