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 ?
where the function set {[q.sub.1] (x), [q.sub.2](x), ..., [q.sub.m](x)} canbe termed a weighted orthogonal function set with weight functions {[w.sub.i]} about points {[x.sub.i]}.
The empirical orthogonal function (EOF) was applied to examine oceanographic parameters quantitatively.
The MSE of the orthogonal function expansion has been shown to be 5, 6, 11]
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].sub.n] (t) series expansion, this expansion method is the KL expansion.
(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 this study, prior information on increasing/decreasing vegetation spatial coverages is calculated by empirical orthogonal function (EOF).
Then we use empirical orthogonal function (EOF) decomposition and geostatistical analysis method to analyze spatial and temporal patterns associated with precipitation.
"Detection of Decreasing Vegetation Cover Based on Empirical Orthogonal Function and Temporal Unmixing Analysis" by D.
The proper orthogonal decomposition (POD) , also known as the Karhunen-Loeve (K-L) decomposition, principal component analysis (PCA), and empirical orthogonal function analysis (EOF) can facilitate the modal projections of partial differential equations into reduced-order models, via a Galerkin projection .
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.
Obled, "On the use of Empirical Orthogonal Function (EOF) analysis in the simulation of random fields," Stochastic Hydrology and Hydraulics, vol.

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