GSVD

GSVD

The generalized singular value decomposition (GSVD) is a mathematical technique used to decompose a matrix pair (A, L) into its constituent parts. It is a generalization of the singular value decomposition (SVD) of A, where the generalized singular values of (A, L) are the square roots of the generalized eigenvalues of the matrix pair (ATA, LTL). This technique is useful in various applications, including signal processing, control theory, and data analysis.From: Damage Models and Algorithms for Assessment of Structures under Operating Conditions [2019]

Subspace Algorithms

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Published in Philipos C. Loizou, Speech Enhancement, 2013

Philipos C. Loizou

Therefore, working with the GSVD of Y and D is mathematically equivalent to working with the SVD of Y–. In other words, the whitening operation is implicitly embedded in the GSVD of Y and D. Hence, the GSVD reduces the two steps (computation of R−1 followed by the matrix product YR−1) required to compute the SVD of the transformed matrix Y– to a single step.

Current distribution reconstruction in switching arcs by means of regularization based on GSVD

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Published in Inverse Problems in Science and Engineering, 2021

Hongchen Zhao, Xiaoming Liu, Hai Chen, Peiyuan Li

The GSVD method is the general-form of the SVD. The generalized singular values of the matrix pair (A, L) are the square roots of the matrix pair . The matrix L must have the same column number as A, and if , the dimensions must satisfy the relation . The GSVD of underdetermined systems is to some extent more complicated than the overdetermined ones and given by Equation (15): where , , , and are orthonormal column matrices, and is nonsingular. The matrices and are order diagonal matrices whose diagonal elements satisfy and are ordered as:

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Current distribution reconstruction in switching arcs by means of regularization based on GSVD