id: 06455424
dt: j
an: 2015e.00921
au: Yang, Yajun; Gordon, Sheldon P.
ti: Interpolation and polynomial curve fitting.
so: Math. Teach. (Reston) 108, No. 2, 132-141 (2014).
py: 2014
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: N50 K80
ut: interpolation; curve fittig; polynomials; Newton interpolation; Lagrange
interpolation; polynomial regression
ci:
li: http://www.nctm.org/publications/article.aspx?id=43017
ab: Summary: Two points determine a line. Three noncollinear points determine a
quadratic function. Four points that do not lie on a lower-degree
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)
rv: