orthogonal functions

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orthogonal functions

[ȯr′thäg·ən·əl ′fəŋk·shənz]
(mathematics)
Two real-valued functions are orthogonal if their inner product vanishes.
References in periodicals archive ?
Obled, "On the use of Empirical Orthogonal Function (EOF) analysis in the simulation of random fields," Stochastic Hydrology and Hydraulics, vol.
Identification of Flexible Robot Arm System Using Extended Volterra Series by Laguerre Orthogonal Function.
The empirical orthogonal function (EOF) was applied to examine oceanographic parameters quantitatively.
A non-periodic random process cannot have unrelated random Fourier coefficients of the Fourier series representation, but the relationship can be used with a number of mutually orthogonal function [[phi].
10) and (11) will cause an underestimation of the variances of the plane parameters fitted with the orthogonal function for large AOI.
It brings together a wide set of material from classical orthogonal function approximation, neural network input-output approximation, finite element methods for distributed parameter systems, and various approximation methods used in adaptive control and learning theory.
In the IMLS approximation, the orthogonal function system is chosen as the basis function, and the resulting algebraic equation system is not ill-conditioned any more.
The book brings together ideas from classical orthogonal function approximation, neural network input-output approximation, finite element methods for distributed parameter systems, and various approximation methods employed in adaptive control and learning theory.
Reasons for using orthogonal functions inside neural networks are stability and tracking performances improvement--which these functions could provide to a system [22].
After reviewing the principles of orthogonal functions and Walsh analysis, this graduate textbook explores the suitability of Walsh functions for the analysis of power electronic systems.
To remedy this, the projection of the field at the boundaries onto orthogonal functions prior to reduction was proposed in [5,10].
Kozlov, On the complete systems of orthogonal functions [in Russian], Mat.

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