Editing Clenshaw algorithm (section)

In [[numerical analysis]], the '''Clenshaw algorithm''', also called '''Clenshaw summation''', is a [[Recursion|recursive]] method to evaluate a linear combination of [[Chebyshev polynomials]].<ref name="Clenshaw55">{{Cite journal | last1 = Clenshaw | first1 = C. W.| title = A note on the summation of Chebyshev series| url = https://www.ams.org/journals/mcom/1955-09-051/S0025-5718-1955-0071856-0/| doi = 10.1090/S0025-5718-1955-0071856-0| journal = Mathematical Tables and Other Aids to Computation| issn = 0025-5718| volume = 9| issue = 51| page = 118| date=July 1955 | doi-access = free}}  Note that this paper is written in terms of the ''Shifted'' Chebyshev polynomials of the first kind <math>T^*_n(x) = T_n(2x-1)</math>.</ref><ref name="Tscherning82"/>  The method was published by [[Charles William Clenshaw]] in 1955. It is a generalization of [[Horner's method]] for evaluating a linear combination of [[monomial]]s.

It generalizes to more than just Chebyshev polynomials; it applies to any class of functions that can be defined by a three-term [[recurrence relation]].<ref>{{Citation |last1=Press |first1=WH |last2=Teukolsky |first2=SA |last3=Vetterling |first3=WT |last4=Flannery |first4=BP |year=2007 |title=Numerical Recipes: The Art of Scientific Computing |edition=3rd |publisher = Cambridge University Press |publication-place=New York |isbn=978-0-521-88068-8 |chapter=Section 5.4.2. Clenshaw's Recurrence Formula |chapter-url=http://apps.nrbook.com/empanel/index.html?pg=222}}</ref>