In numerical analysis, the Clenshaw algorithm, also called Clenshaw summation, is a recursive method to evaluate a linear combination of Chebyshev polynomials...

plotted below: Bézier curves De Boor's algorithm Horner scheme to evaluate polynomials in monomial form Clenshaw algorithm to evaluate polynomials in Chebyshev...

Suanjing. Clenshaw algorithm to evaluate polynomials in Chebyshev form De Boor's algorithm to evaluate splines in B-spline form De Casteljau's algorithm to evaluate...

the polynomial into the Chebyshev form and evaluating it with the Clenshaw algorithm). Algebraic operations can be done readily on the power series representation;...

such an algorithm was put forward by C. W. Clenshaw and F. W. J. Olver in a paper published in 1980. In the problem of developing algorithms for computing...

He is known for the Clenshaw algorithm (1955) and Clenshaw–Curtis quadrature (1960). In a 1984 paper Beyond Floating Point, Clenshaw and Frank W. J. Olver...

Fourier transform-related algorithms for the DCT. A simple way of understanding the algorithm is to realize that Clenshaw–Curtis quadrature (proposed...

parallelization Clenshaw algorithm De Casteljau's algorithm Square roots and other roots: Integer square root Methods of computing square roots nth root algorithm hypot...

_{n=0}^{N}a_{n}T_{n}(x).} Polynomials in Chebyshev form can be evaluated using the Clenshaw algorithm. Polynomials denoted C n ( x ) {\displaystyle C_{n}(x)} and S n (...

which is solved by the QR algorithm. This algorithm was popular, but significantly more efficient algorithms exist. Algorithms based on the Newton–Raphson...

can use Clenshaw algorithm. For polynomials in Bézier form we can use De Casteljau's algorithm, and for B-splines there is De Boor's algorithm. The fact...

(LI) representation of numbers, and its algorithms for arithmetic operations, were introduced by Charles Clenshaw and Frank Olver in 1984. The symmetric...

In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral. The term numerical...

unequally spaced points, then other methods such as Gaussian quadrature and Clenshaw–Curtis quadrature are generally more accurate. The method is named after...

Chebyshev approximation is the basis for Clenshaw–Curtis quadrature, a numerical integration technique. The Remez algorithm (sometimes spelled Remes) is used...

evaluated can be re-used upon recursion: A similar strategy is used with Clenshaw–Curtis quadrature, where the nodes are chosen as x i = cos ⁡ ( 2 i n π...

adaptive algorithm for numerical integration to appear in print, although more modern adaptive methods based on Gauss–Kronrod quadrature and Clenshaw–Curtis...

fast DCT algorithms (below) are used in Chebyshev approximation of arbitrary functions by series of Chebyshev polynomials, for example in Clenshaw–Curtis...

complex. The (symmetric) level-index arithmetic (LI and SLI) of Charles Clenshaw, Frank Olver and Peter Turner is a scheme based on a generalized logarithm...

Filon-type integration methods. These include Filon-trapezoidal and Filon–Clenshaw–Curtis methods. Filon quadrature is widely used in physics and engineering...

jl (which can compute Gauss–Kronrod formulas to arbitrary precision). Clenshaw–Curtis quadrature, another nested quadrature rule with similar accuracy...

inaccuracy due to Runge's phenomenon. One solution to this problem is Clenshaw–Curtis quadrature, in which the integrand is approximated by expanding...

Péter, which does not form a hyperoperation hierarchy. In 1984, C. W. Clenshaw and F. W. J. Olver began the discussion of using hyperoperations to prevent...

and Gerhard Fettweis, "Computation of forward and inverse MDCT using Clenshaw's recurrence formula," IEEE Trans. Sig. Proc. 51 (5), 1439-1444 (2003) Che-Hong...

The trigonometric series given above can be conveniently evaluated using Clenshaw summation. This method avoids the calculation of most of the trigonometric...