
06526676
j
2016a.00948
Vajda, R\'obert
Exploring Hermite interpolation polynomials using recursion.
Ann. Math. Inform. 45, 151160 (2015).
2015
Eszterh\'azy K\'aroly College, Institute of Mathematics and Computer Science, Eger
EN
N55
U75
Hermite interpolation
Neville's recursion
divided differences
linear algebra
interpolation sequence
enumeration
computer supported learning environment
Mathematica
Summary: Summary. In this paper we consider the teaching of Hermite interpolation. We propose here two nonstandard approaches for exploring Hermite interpolation polynomials in a computer supported environment. As an extension to the standard construction of the interpolation polynomials based on either on the fundamental polynomials or the triangular shaped divided difference table, we first investigate the generalization of the Neville type recursive scheme which may be familiar to the reader or to the student from the chapter about Lagrangian interpolation. Second, we propose an interactive demo tool where by the stepbystep construction of the interpolation polynomial, the interpolation constraints can be considered in an almost arbitrary order. Thus the same interpolating polynomial can be constructed in several different ways. As a byproduct, one can also ask an interesting combinatorial problem from the students about the number of compatible orders of the constraints depending on the cardinality of node system.