Matrix Transformations and Disk of Convergence in Interpolation Processes
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, C...
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| Format: | Article |
| Language: | English |
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2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/905635 |
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| author | Chikkanna R. Selvaraj Suguna Selvaraj |
| author_facet | Chikkanna R. Selvaraj Suguna Selvaraj |
| author_sort | Chikkanna R. Selvaraj |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ec553debdfc148c7bca477f03902e5aa |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ec553debdfc148c7bca477f03902e5aa2025-02-03T06:42:00ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/905635905635Matrix Transformations and Disk of Convergence in Interpolation ProcessesChikkanna R. Selvaraj0Suguna Selvaraj1Department of Mathematics, Pennsylvania State University, Shenango Campus, 147 Shenango Avenue, Sharon, PA 16146, USADepartment of Mathematics, Pennsylvania State University, Shenango Campus, 147 Shenango Avenue, Sharon, PA 16146, USALet 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.http://dx.doi.org/10.1155/2008/905635 |
| spellingShingle | Chikkanna R. Selvaraj Suguna Selvaraj Matrix Transformations and Disk of Convergence in Interpolation Processes International Journal of Mathematics and Mathematical Sciences |
| title | Matrix Transformations and Disk of Convergence in Interpolation Processes |
| title_full | Matrix Transformations and Disk of Convergence in Interpolation Processes |
| title_fullStr | Matrix Transformations and Disk of Convergence in Interpolation Processes |
| title_full_unstemmed | Matrix Transformations and Disk of Convergence in Interpolation Processes |
| title_short | Matrix Transformations and Disk of Convergence in Interpolation Processes |
| title_sort | matrix transformations and disk of convergence in interpolation processes |
| url | http://dx.doi.org/10.1155/2008/905635 |
| work_keys_str_mv | AT chikkannarselvaraj matrixtransformationsanddiskofconvergenceininterpolationprocesses AT sugunaselvaraj matrixtransformationsanddiskofconvergenceininterpolationprocesses |