Clenshaw algorithm Guide, Meaning , Facts, Information and Description

In the mathematical subfield of numerical analysis the Clenshaw algorithm is a recursive method to evaluate polynomials in Chebyshev form.

Table of contents

1 Polynomial in Chebyshev form 2 Clenshaw algorithm 3 See also

Polynomial in Chebyshev form

A polynomial of degree N in Chebyshev form is a polynomial p(x) of the form

where T_n is the nth Chebyshev polynomial.

Clenshaw algorithm

The Clenshaw algorithm can be used to evaluate a polynomial in the Chebyshev form. Given

we define

then

See also

• Horner scheme to evaluate polynomials in monomial form
• De Casteljau's algorithm to evaluate polynomials in Bézier form

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