
06455424
j
2015e.00921
Yang, Yajun
Gordon, Sheldon P.
Interpolation and polynomial curve fitting.
Math. Teach. (Reston) 108, No. 2, 132141 (2014).
2014
National Council of Teachers of Mathematics (NCTM), Reston, VA
EN
N50
K80
interpolation
curve fittig
polynomials
Newton interpolation
Lagrange interpolation
polynomial regression
http://www.nctm.org/publications/article.aspx?id=43017
Summary: Two points determine a line. Three noncollinear points determine a quadratic function. Four points that do not lie on a lowerdegree polynomial curve determine a cubic function. In general, $n + 1$ points uniquely determine a polynomial of degree $n$, presuming that they do not fall onto a polynomial of lower degree. The process of finding such a polynomial is called interpolation, and the two most important approaches used are Newton's and Lagrange's interpolating formulas. Each has its advantages and disadvantages, as we will discuss. In this article, we show how both approaches can be introduced and developed at the precalculus level in the context of fitting polynomials to data. These methods bring some of the most powerful and useful tools of numerical analysis to the attention of students who are still at the introductory level while building on and reinforcing many fundamental ideas in algebra and precalculus mathematics. (ERIC)