A construction algorithm for dual complex generalized eigenvalue decomposition and its application to blind source separation

Since the generalized eigenvalue problem has a unique and stable solution when the generalized eigenvalues are distinct, which is fundamental to many scientific and engineering applications, in this paper, we study the dual complex generalized eigenvalue decomposition under the condition of distinct...

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Bibliographic Details
Published in:	Signal processing Vol. 240; p. 110342
Main Authors:	Wang, Tao, Li, Ying, Zhang, Mingcui
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.03.2026
Subjects:	Blind source separation Construction algorithm Dual complex matrix Generalize eigenvalue decomposition Construction algorithm Blind source separation Dual complex matrix Generalize eigenvalue decomposition 15B33
ISSN:	0165-1684
Online Access:	Get full text
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Summary:	Since the generalized eigenvalue problem has a unique and stable solution when the generalized eigenvalues are distinct, which is fundamental to many scientific and engineering applications, in this paper, we study the dual complex generalized eigenvalue decomposition under the condition of distinct standard parts of the generalized eigenvalues. By using the special properties of the dual complex matrix, we establish a sufficient condition for realizing the dual complex generalized eigenvalue decomposition, and transform the dual complex generalized eigenvalue decomposition problem into the equivalent generalized eigenvalue decomposition problem and the dual part construction problem over the complex field. By solving these two problems, we propose a construction algorithm for dual complex generalized eigenvalue decomposition under the condition of distinct standard parts of the generalized eigenvalues. We verify the effectiveness, accuracy and numerical stability of the algorithm by experiment. In addition, we propose a dual complex color image model. Based on this model, we propose a blind source separation algorithm for color images, and show that it has good separation performance for cross-channel mixed color images by experiment.
ISSN:	0165-1684
DOI:	10.1016/j.sigpro.2025.110342