J -spectral Factorization via Similarity Transformations
نویسنده
چکیده
Abstract This paper characterizes a class of regular para-Hermitian transfer matrices and then studies the J-spectral factorization of this class using similarity transformations. A transfer matrix Λ in this class admits a J-spectral factorization if and only if there exists a common nonsingular matrix to similarly transform the A-matrices of Λ and Λ, resp., into 2 × 2 lower (upper, resp.) triangular block matrices with the (1, 1)-block including all the stable modes of Λ (Λ, resp.). For a transfer matrix in a smaller subset, this nonsingular matrix is formulated in terms of the stabilizing solutions of two algebraic Riccati equations. The Jspectral factor is formulated in terms of the original realization of the transfer matrix. Copyright c ©2005 IFAC.
منابع مشابه
Hyperspectral Image Classification Based on the Fusion of the Features Generated by Sparse Representation Methods, Linear and Non-linear Transformations
The ability of recording the high resolution spectral signature of earth surface would be the most important feature of hyperspectral sensors. On the other hand, classification of hyperspectral imagery is known as one of the methods to extracting information from these remote sensing data sources. Despite the high potential of hyperspectral images in the information content point of view, there...
متن کاملDiscrete Spectral Transformations of Skew Orthogonal Polynomials and Associated Discrete Integrable Systems
Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension. Especially in the (2+1)dimensional case, the corresponding system can be extended to 2 × 2 matrix form. The factorization theorem of the Christoffel kernel for s...
متن کاملFactorization of non-linear supersymmetry in one-dimensional Quantum Mechanics. II: proofs of theorems on reducibility
In this paper, we continue to study factorization of supersymmetric (SUSY) transformations in one-dimensional Quantum Mechanics into chains of elementary Darboux transformations with nonsingular coefficients. We define the class of potentials that are invariant under the Darboux – Crum transformations and prove a number of lemmas and theorems substantiating the formulated formerly conjectures o...
متن کاملA unification of unitary similarity transforms to compressed representations
A new framework for transforming arbitrary matrices to compressed representations is presented. The framework provides a generic way of transforming a matrix via unitary similarity transformations to e.g. Hessenberg, Hessenberg-like and combinations of both. The new algorithms are deduced, based on the QR-factorization of the original matrix. Based on manipulations with Givens transformations, ...
متن کاملSymNMF: nonnegative low-rank approximation of a similarity matrix for graph clustering
Nonnegative matrix factorization (NMF) provides a lower rank approximation of a matrix by a product of two nonnegative factors. NMF has been shown to produce clustering results that are often superior to those by other methods such as K-means. In this paper, we provide further interpretation of NMF as a clustering method and study an extended formulation for graph clustering called Symmetric NM...
متن کامل