On multivariable matrix spectral factorization method
نویسندگان
چکیده
Spectral factorization is a prominent tool with several important applications in various areas of applied science. Wiener and Masani proved the existence matrix spectral factorization. Their theorem has been extended to multivariable case by Helson Lowdenslager. Solving problem numerically challenging both situations, also due its practical applications. Therefore, authors have developed algorithms for The Janashia-Lagvilava algorithm relatively new method which be useful In this paper, we extend case. Consequently, numerical constructed.
منابع مشابه
The Spectral Factorization Problem for Multivariable Distributed Parameter Systems
This paper studies the solution of the spectral factorization problem for multivariable distributed parameter systems with an impulse response having an in nite number of delayed impulses. A coercivity criterion for the existence of an invertible spectral factor is given for the cases that the delays are a) arbitrary (not necessarily commensurate) and b) equally spaced (commensurate); for the l...
متن کاملNonnegative Matrix Factorization for Spectral Data Analysis
Data analysis is pervasive throughout business, engineering and science. Very often the data to be analyzed is nonnegative, and it is often preferable to take this constraint into account in the analysis process. Here we are concerned with the application of analyzing data obtained using astronomical spectrometers, which provide spectral data which is inherently nonnegative. The identification ...
متن کاملOn the Equivalence of Nonnegative Matrix Factorization and Spectral Clustering
Current nonnegative matrix factorization (NMF) deals with X = FG type. We provide a systematic analysis and extensions of NMF to the symmetric W = HH , and the weighted W = HSH . We show that (1) W = HH is equivalent to Kernel K-means clustering and the Laplacian-based spectral clustering. (2) X = FG is equivalent to simultaneous clustering of rows and columns of a bipartite graph. Algorithms a...
متن کاملArea-Correlated Spectral Unmixing Based on Bayesian Nonnegative Matrix Factorization
To solve the problem of the spatial correlation for adjacent areas in traditional spectral unmixing methods, we propose an area-correlated spectral unmixing method based on Bayesian nonnegative matrix factorization. In the proposed method, the spatial correlation property between two adjacent areas is expressed by a priori probability density function, and the endmembers extracted from one of t...
متن کاملSpectral Factorization of Non-Rational Matrix-Valued Spectral Densities
Recently, a necessary and sufficient uniform log-integrability condition has been established for the canonical spectral factorization mapping to be sequentially continuous. Under this condition, if a sequence of spectral densities converge to a limiting spectral density then the canonical spectral factors of the sequence converges to the canonical spectral factor of the limiting density. Howev...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2022
ISSN: ['0022-247X', '1096-0813']
DOI: https://doi.org/10.1016/j.jmaa.2022.126300