Clenshaw Algorithm
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A Clenshaw Algorithm is a Polynomial Evaluation Algorithm that is a recursive algorithm that evaluates a linear combination of Chebyshev polynomials.
- AKA: Clenshaw Summation Algorithm.
- Example(s):
- Counter-Example(s):
- See: Recurrence Relation, Numerical Analysis, Recursion, Chebyshev Polynomials, Charles William Clenshaw, Monomial.
References
2021
- (Wikipedia, 2021) ⇒ https://en.wikipedia.org/wiki/Clenshaw_algorithm Retrieved:2021-9-5.
- In numerical analysis, the Clenshaw algorithm, also called Clenshaw summation, is a recursive method to evaluate a linear combination of Chebyshev polynomials.[1] [2] The method was published by Charles William Clenshaw in 1955. It is a generalization of Horner's method for evaluating a linear combination of monomials.
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.
- In numerical analysis, the Clenshaw algorithm, also called Clenshaw summation, is a recursive method to evaluate a linear combination of Chebyshev polynomials.[1] [2] The method was published by Charles William Clenshaw in 1955. It is a generalization of Horner's method for evaluating a linear combination of monomials.
- ↑ Note that this paper is written in terms of the Shifted Chebyshev polynomials of the first kind [math]\displaystyle{ T^*_n(x) = T_n(2x-1) }[/math] .
- ↑ Tscherning, C. C.; Poder, K. (1982), "Some Geodetic applications of Clenshaw Summation" (PDF), Bolletino di Geodesia e Scienze Affini, 41 (4): 349–375,
2002
- (Holmes & Featherstone, 2002) ⇒ S. A. Holmes, and W. E. Featherstone (2002). "A Unified Approach To The Clenshaw Summation And The Recursive Computation Of Very High Degree And Order Normalised Associated Legendre Functions". In: Journal of Geodesy, 76(5), 279-299.
1982
- (Tscherning & Poder, 1982) ⇒ C.C. Tscherning, and K. Poder (1982). "Some Geodetic Applications of Clenshaw Summation (*)". In: Bollettino Di Geodesia e Scienze Affini - Anno XLI,N.4.