### Abstract

Let A_{ρ} 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) ∈ A_{ρ} 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 language | English (US) |
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Article number | 905635 |

Journal | International Journal of Mathematics and Mathematical Sciences |

Volume | 2008 |

DOIs | |

State | Published - Dec 30 2008 |

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### All Science Journal Classification (ASJC) codes

- Mathematics (miscellaneous)

### Cite this

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*International Journal of Mathematics and Mathematical Sciences*, vol. 2008, 905635. https://doi.org/10.1155/2008/905635

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Matrix transformations and disk of convergence in interpolation processes

AU - Selvaraj, Chikkanna R.

AU - Selvaraj, Suguna

PY - 2008/12/30

Y1 - 2008/12/30

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=57949094101&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57949094101&partnerID=8YFLogxK

U2 - 10.1155/2008/905635

DO - 10.1155/2008/905635

M3 - Article

AN - SCOPUS:57949094101

VL - 2008

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

SN - 0161-1712

M1 - 905635

ER -