orthogonalization


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orthogonalization

[ȯr‚thäg·ə·nə·lə′zā·shən]
(mathematics)
A procedure in which, given a set of linearly independent vectors in an inner product space, a set of orthogonal vectors is recursively obtained so that each set spans the same subspace.
References in periodicals archive ?
m] denotes the Gram-Schmidt orthogonalization of the vectors [s.
Sims (1980) made the assumption about orthogonalization of the reduced form innovations done through Cholesky decomposition, which needs a causal ordering relating to how the system works (Cooley & Leroy).
This innovative achievement can effectively resolve congestion in LTE networks with 3D beamforming, accurate channel calibration, intelligent orthogonalization, advanced power distribution, and other cutting-edge technologies.
Simultaneous Expansion and Orthogonalization of Measured Modes for Structure Identification.
Impulse response functions based on a causal approach to residual orthogonalization in vector autoregressions.
For robustness, we reverse the orthogonalization procedure and include the Democrat index and the residual Republican index in the regression.
PCA involved several calculations utilizing orthogonalization procedures, such as singular-value decomposition, eigenvector calculation with the use of a covariant matrix, nonlinear iterative partial least squares, and successive average orthogonalization (Donahue and Brown 1991, Malinowski 1991, Hasegawa 1999).
According to Clayton and Mackinnon (2013), the pure form of variables was extracted through orthogonalization method, which consists in regressing each return variable, in this case RRE (real estate) and RB (bonds) against the other return factors.
Because the basis vectors are linearly dependent, Gram Schmidt orthogonalization must be performed to avoid numerical errors.
To avoid numerical errors from this dependency, Gram-Schmidt orthogonalization must be performed.
The orthogonalization coefficients are stored in the mth column of [B.
Tugnait, "Time-varying channel estimation using two dimensional channel orthogonalization and superimposed training", IEEE Trans, on Signal Process.

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