TY - JOUR
T1 - Explicit Hermite Interpolation Polynomials via the Cycle Index with Applications
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 - <p style="text-align: justify;">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&#39;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.</p>