Open Access
Generalized singular value decompositions: a proposal for a standardized nomenclature
Bart De Moor,Gene H. Golub +1 more
Reads0
Chats0
TLDR
An alphabetic and mnemonic system of names for several matrix decompositions related to the singular value decomposition is proposed: the OSVD, PSVD, QSVD, RSVD, SSVD, TSVD.Abstract:
An alphabetic and mnemonic system of names for several matrix decompositions related to the singular value decomposition is proposed: the OSVD, PSVD, QSVD, RSVD, SSVD, TSVD. The main purpose of this note is to propose a standardization of the nomenclature and the structure of these matrix decompositions.read more
Citations
More filters
Journal ArticleDOI
Subspace algorithms for the stochastic identification problem
Peter Van Overschee,Bart De Moor +1 more
TL;DR: A new subspace algorithm is derived to consistently identify stochastic state space models from given output data without forming the covariance matrix and using only semi-infinite block Hankel matrices.
Proceedings ArticleDOI
Subspace algorithms for the stochastic identification problem
P. Van Overschee,B. De Moor +1 more
TL;DR: In this article, the authors derive a novel algorithm to consistently identify stochastic state space models from given output data without forming the covariance matrix and using only semi-infinite block Hankel matrices.
Journal ArticleDOI
The singular value decomposition and long and short spaces of noisy matrices
TL;DR: It is clarified why and when the singular value decomposition is successful in so-called subspace methods and an expression is found for the asymptotic bias in terms of canonical angles, which can be estimated from the data.
Journal ArticleDOI
Computing the generalized singular value decomposition
Zhaojun Bai,James Demmel +1 more
TL;DR: A new numerical method for computing the GSVD of two matrices A and B is presented, a variation on Paige''s method, which differs from previous algorithms in guaranteeing both backward stability and convergence.
Journal ArticleDOI
A tree of generalizations of the ordinary singular value decomposition
Bart De Moor,Hongyuan Zha +1 more
TL;DR: It is shown how to generalize the ordinary singular value decomposition of a matrix into a combined factorization of any number of matrices, and proposed to call these factorizations generalized singularvalue decompositions.
References
More filters
Analysis of feedback systems with structured uncertainties
TL;DR: In this article, a general approach for analysing linear systems with structured uncertainty based on a new generalised spectral theory for matrices is introduced, which naturally extend techniques based on singular values and eliminate their most serious difficulties.
Journal ArticleDOI
Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms
TL;DR: It is shown that a similar approach may be taken, involving the generalized singular value decomposition of a certain product of matrices without explicitly forming the product, to the classical simultaneous diagonalization problem.
Journal ArticleDOI
Generalizing the Singular Value Decomposition
TL;DR: Two generalizations of the singular value decomposition are given in this article, and these generalizations provided a unified way of regarding certain matrix problems and the numerical techniques which are used to solve them.
Journal ArticleDOI
Towards a Generalized Singular Value Decomposition
TL;DR: The generalized singular value decomposition of any two matrices having the same number of columns has been studied in this paper, where a form for, and a constructive derivation of, the generalized singular values decomposition for any two vectors having columns is given.