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Volume 5, Issue 3
Explicit Hermite Interpolation Polynomials via the Cycle Index with Applications

F. J. Hickernell & S. Yang

Int. J. Numer. Anal. Mod., 5 (2008), pp. 457-465.

Published online: 2008-05

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  • Abstract

The cycle index polynomial of a symmetric group is a basic tool in combinatorics and especially in Pόlya enumeration theory. It seems irrelevant to numerical analysis. Through Faá di Bruno's formula, cycle index is connected with numerical analysis. In this work, the Hermite interpolation polynomial is explicitly expressed in terms of cycle index. Applications in Gauss-Turán quadrature formula are also considered.

  • Keywords

symmetric group, cycle index polynomial, Faá di Bruno's formula, Bell's polynomial, Hermite interpolation polynomial, Gauss-Turán quadrature formula.

  • AMS Subject Headings

05A15, 65D05, 65D32

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-5-457, author = {F. J. Hickernell and S. Yang}, title = {Explicit Hermite Interpolation Polynomials via the Cycle Index with Applications}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2008}, volume = {5}, number = {3}, pages = {457--465}, abstract = {

The cycle index polynomial of a symmetric group is a basic tool in combinatorics and especially in Pόlya enumeration theory. It seems irrelevant to numerical analysis. Through Faá di Bruno's formula, cycle index is connected with numerical analysis. In this work, the Hermite interpolation polynomial is explicitly expressed in terms of cycle index. Applications in Gauss-Turán quadrature formula are also considered.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/821.html} }
TY - JOUR T1 - Explicit Hermite Interpolation Polynomials via the Cycle Index with Applications AU - F. J. Hickernell & S. Yang JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 457 EP - 465 PY - 2008 DA - 2008/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/821.html KW - symmetric group, cycle index polynomial, Faá di Bruno's formula, Bell's polynomial, Hermite interpolation polynomial, Gauss-Turán quadrature formula. AB -

The cycle index polynomial of a symmetric group is a basic tool in combinatorics and especially in Pόlya enumeration theory. It seems irrelevant to numerical analysis. Through Faá di Bruno's formula, cycle index is connected with numerical analysis. In this work, the Hermite interpolation polynomial is explicitly expressed in terms of cycle index. Applications in Gauss-Turán quadrature formula are also considered.

F. J. Hickernell and S. Yang. (2008). Explicit Hermite Interpolation Polynomials via the Cycle Index with Applications. International Journal of Numerical Analysis and Modeling. 5 (3). 457-465. doi:
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