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 ?
Peak used empirical orthogonal functions, or principal components, to condense band shape into just a few (five) coefficients.
Zhou, "A new unconditionally stable scheme for FDTD method using associated Hermite orthogonal functions," IEEE Transactions on Antennas and Propagation, vol.
Reasons for using orthogonal functions inside neural networks are stability and tracking performances improvement--which these functions could provide to a system [22].
We notice that the problem of optimum choice of the free parameter of some orthogonal functions (Laguerre, Kautz) for the conventional system modeling has already been reported by many researchers [6,7,11,15,18,24].
Some methods to do this are recursive algorithm [24], utilizing Gaussian input [24], Gradient-based search [25], Cross correlation method [26], Hilbert space reproduced kernel method [19, 20], expansion with orthogonal functions [27-30] etc.
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.
In recent years, some orthogonal functions have been utilized in the corresponding theoretical investigations.
Piroozfar, "Numerical solution of the linear two-dimensional Fredholm integral equations of the second kind via two-dimensional triangular orthogonal functions," Journal of King Saud University - Science, vol.
In Section 2, the MLS approximation with orthogonal functions is reviewed.
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.
EOF analysis is a useful technique for decomposition of a time series of geophysical data into temporal and spatial variability in terms of orthogonal functions or statistical modes.

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