# spectral approximation

## spectral approximation

[‚spek·trəl ə‚prȧk·sə′mā·shən]
(mathematics)
A numerical approximation of a function of two or more variables that involves the expansion of the function into a generalized Fourier series, followed by computation of the Fourier coefficients.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Zhu, Laguerre pseudo Spectral approximation to the Thomas-Fermi equation, J.
Property 4) defines the truncated spectral approximation of the L matrix, that considers the contribution of the first k eigenpairs related to the smallest eigenvalues, which hold for identifying the main shape features at different scale forming a signature for shape characterization.
develop a spectral approximation method to distributed thermal processing, and a hybrid general regression NN is trained to be a nonlinear model of the original PDE, which also allows many control methods to be applied to this kind of nonlinear PDEs.
Heinrichs, "Spectral approximation of third-order problems," Journal of Scientific Computing, vol.
The time-splitting Chebyshev-spectral method is based on Strang splitting method in time coupled with Chebyshev- spectral approximation in space.
The frequently studied Gegenbauer reconstruction method has been shown to alleviate the effects of the Gibbs phenomenon while restoring the exponential accuracy of the spectral approximation. Since each reconstruction must be implemented only within smooth regions, the jump discontinuities of the piecewise smooth function must first be located by an edge detection method.
Since monomials are highly collinear and determinist integration schemes are preferred for low dimensional problems over montecarlo approaches (Geweke, 1996), we stick with Chebyshev polynomials as our favorite spectral approximation. See Christiano and Fisher (2000) for a thorough explanation.
From the overview of spectral approximation to differential equations, the spectral methods have been divided to four types, namely, collocation [9-11], tau [12, 13], Galerkin [14, 15], and Petrov Galerkin [16, 17] methods.
HUANG, A time-space collocation spectral approximation for a class of time fractional differential equations, Int.
CHATELIN, Spectral Approximation of Linear Operators, Academic Press, New York, 1983.
OSBORN, Spectral approximation for compact operators, Math.
In this paper we present an extension of the spectral approximation theory for non-compact operators in Hilbert spaces.
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