Chebyshev approximation

Chebyshev approximation

(mathematics)
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The motive of this paper is to develop a hybrid interval procedure based on the Chebyshev approximation for transient calculation of rotors.
Kollar, "Crest-factor minimization using nonlinear Chebyshev approximation methods", IEEE Trans.
We now wish to prove the continuity and coercivity of the least squares functionals for the Chebyshev approximation. First we assume that an a priori estimate (2.14) holds for the Stokes equation in [[ohm].sub.S], that is
Caption: Figure 11: Forced vibration response of an isotropic rod of free ends within a frequency band from 200 kHz to 250 kHz for Chebyshev approximation polynomials--a numerical model of 736 DOFs according to the elementary theory of rods [36], based on Chebyshev node distribution used for calculations by the TD-FEM (c = 5 km/s, L = 5 m).
Following this concept, ROM-less DDFS have been reported based on a special phase conversion algorithm such as a Taylors series evaluation as in [2], a coordinate rotation digital computer (CORDIC) algorithm as in [3], a first-order Chebyshev approximation as in [4, 5], a piecewise firstorder polynomial approximation as in [6, 7], a second-order parabolic approximation as in [8], a two-segment fourthorder parabolic approximation [9], and an eighth-order even polynomial as in [10], among others.
Table 4 also shows the spectral convergence in [L.sup.2.sub.w]([OMEGA]- and [H.sup.1.sub.w]([OMEGA])-norm errors of Legendre and Chebyshev approximation. The exact solution, approximated one, and its error for the Legendre case of this example are plotted in Figure 4.
In this section, we provide a common step by step design for a band pass waveguide filter based on Chebyshev approximation. The approximate center frequency is located at 9.25 GHz and the filter bandwidth is about 1.5 GHz, the ripple in pass band is 0.5 dB.
They proceed to fully explain the L1 approximation, including bounded variables and plane curves, the Chebyshev approximation, least squared approximations, and under-determines systems of linear equations.
The mth Chebyshev approximation to the system output y(t) can be obtained directly from (8).
McClellan, "Chebyshev approximation for non-recursive digital filters with linear phase", IEEE Trans.