On minor prime factorizations for multivariate polynomial matrices

Multivariate polynomial matrix factorizations have been widely investigated during the past years due to the fundamental importance in the areas of multidimensional systems and signal processing. In this paper, minor prime factorizations for multivariate polynomial matrices are studied. We give a ne...

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Bibliographic Details
Published inMultidimensional systems and signal processing Vol. 30; no. 1; pp. 493 - 502
Main Authors Guan, Jiancheng, Li, Weiqing, Ouyang, Baiyu
Format Journal Article
LanguageEnglish
Published New York Springer US 01.01.2019
Springer Nature B.V
Subjects
Artificial Intelligence
Circuits and Systems
Electrical Engineering
Engineering
Polynomial matrices
Radon
Signal processing
Signal,Image and Speech Processing
Multidimensional systems
Matrix factorizations
Multivariate polynomial matrices
Minor prime factorizations
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Summary:Multivariate polynomial matrix factorizations have been widely investigated during the past years due to the fundamental importance in the areas of multidimensional systems and signal processing. In this paper, minor prime factorizations for multivariate polynomial matrices are studied. We give a necessary and sufficient condition for the existence of a minor left prime factorization for a multivariate polynomial matrix. This result is a generalization of a theorem in Wang and Kwong (Math Control Signals Syst 17(4):297–311, 2005 ). On the basis of this result and a method in Fabiańska and Quadrat (Radon Ser Comp Appl Math 3:23–106, 2007 ), we give an algorithm to decide if a multivariate polynomial matrix has minor left prime factorizations and compute one if they exist.
Bibliography:ObjectType-Article-1
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ISSN:0923-6082
1573-0824
DOI:10.1007/s11045-018-0566-4