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The Chebyshev polynomials form a complete orthogonal system. The Chebyshev series converges to f(x) if the function is piecewise smooth and continuous. The smoothness requirement can be relaxed in most cases – as long as there are a finite number of discontinuities in f(x) and its derivatives. At a discontinuity, the series will converge to ...
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Clenshaw–Curtis quadrature and Fejér quadrature are methods for numerical integration, or "quadrature", that are based on an expansion of the integrand in terms of Chebyshev polynomials. Equivalently, they employ a change of variables x = cos θ {\displaystyle x=\cos \theta } and use a discrete cosine transform (DCT) approximation for ...
In applied mathematics, a discrete Chebyshev transform (DCT) is an analog of the discrete Fourier transform for a function of a real interval, converting in either direction between function values at a set of Chebyshev nodes and coefficients of a function in Chebyshev polynomial basis. Like the Chebyshev polynomials, it is named after Pafnuty ...
Scarborough is a joint venture between The Nielsen Company and Arbitron. [2] Scarborough began as a subsidiary of VNU and was merged with Birch Radio in 1987. VNU then sold 50% of interest in Scarborough to Arbitron in 1992. VNU was renamed as the Nielsen Company in 2007. [3] Scarborough's major services include: Local market studies in over ...
Nielsen, best known for delivering TV ratings, is getting ready for a future when it gauges a lot more than what people are watching on TV. The media-measurement giant plans to launch a new system ...
Nielsen Media Research is a sister company to Nielsen NetRatings, which measures Internet and digital media audiences through a telephone and internet survey, and Nielsen BuzzMetrics, which measures Consumer-Generated Media. Nielsen also conducts market research for the film industry through National Research Group (NRG).
The Chebyshev nodes of the second kind, also called the Chebyshev extrema, are the extrema of the Chebyshev polynomials of the first kind, which are also the zeros of the Chebyshev polynomials of the second kind. Both of these sets of numbers are commonly referred to as Chebyshev nodes in literature. [1]