Editing Polynomial (section)

=== Interpolation and approximation ===
{{See also|Polynomial interpolation|Orthogonal polynomials|B-spline|spline interpolation}}
The simple structure of polynomial functions makes them quite useful in analyzing general functions using polynomial approximations. An important example in [[calculus]] is [[Taylor's theorem]], which roughly states that every [[differentiable function]] locally looks like a polynomial function, and the [[Stone–Weierstrass theorem]], which states that every [[continuous function]] defined on a [[compact space|compact]] [[interval (mathematics)|interval]] of the real axis can be approximated on the whole interval as closely as desired by a polynomial function.  Practical methods of approximation include [[polynomial interpolation]] and the use of [[spline (mathematics)|splines]].<ref>{{cite book |last=de Villiers |first=Johann |title=Mathematics of Approximation |publisher=Springer |year=2012 |isbn=9789491216503 |url=https://books.google.com/books?id=l5mIro_6RlUC}}</ref>