On multivariate polynomial matrix factorization problems

Mathematics of Control, Signals, and Systems

Volumn 17, Issue 4, 2005, Pages 297-311

  Mingsheng, Wang ^a   Kwong, C P ^b  

^a INSTITUTE OF SOFTWARE   (China)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Matrix factorizations; Minorleft prime; Multi dimensional systems; Multivariate polynomial matrices; Reduced minors; Zero left prime

Indexed keywords

ALGORITHMS; POLYNOMIALS; SIGNAL PROCESSING; SYSTEM THEORY;

MATRIX FACTORIZATIONS; MINOR LEFT PRIME; MULTIDIMENSIONAL SYSTEMS; MULTIVARIATE POLYNOMIAL MATRICES; REDUCED MINORS; ZERO LEFT PRIME;

MATRIX ALGEBRA;

EID: 27244451010     PISSN: 09324194     EISSN: 1435568X     Source Type: Journal    
DOI: 10.1007/s00498-005-0155-6     Document Type: Article

References (18)

1. Charoenlarpnopparut C, Bose NK (1999) Multidimensional FIR filter bank design using Gröbner basis. IEEE Trans. Circuits Syst.-II: Analog Digit Signal Proc 46(12):1475-1486
2. Bose NK (2000) Multivariate matrix factorization for multiband filter banks, wavelets and other n-D problems. In: Proceedings of second international workshop on multidimensional n-D systems, pp 31-38
3. Fornasini E, Valcher ME (1997) n-D polynomial matrices with applications to Multidimensional signal analysis. Multidimensional Syst Signal Proc 8:387-408
4. Greuel GM, Pfister G (2002) A singular introduction to commutative algebra. Springer, Berlin Heidelberg, New York
5. Kung SY, Levy BC, Morf M, Kailath T (1977) New results in 2-D systems theory, Part II: 2-D state space and model-realization and the notions of controllability, observability, and minimality. Proc IEEE 65:945-961
6. Kreuzer M, Robbiano L (2000) Computational commutative algebra I. Springer, Berlin Heidelberg, New York
7. Kleon S, Oberst U (1999) Transfer operators and state spaces for discrete multidimensional linear systems. Acta Applicandae Math 57:1-82
8. Lin Z (1999) Notes on n -D polynomial matrix factorization. Multidimensional Syst Signal Processing 10:379-393
9. Lin Z (2001) Further results on n -D polynomial matrix factorizations. Multidimensional Syst Signal Processing 12:199-208
10. Lin Z, Bose NK (2001) A generalization of Serre's conjecture and related issues. Lin Algebra Appl 338:125-138
11. Morf M, Levy BC, Kung SY (1977) New results in 2-D systems theory, Part I: 2-D polynomial matrices, factorizations and coprimeness. Proc IEEE 65:861-872
12. Pommaret JF (2001) Solving Bose conjecture on linear multidimensional systems. Proc Eur Control Conf pp 1853-1855
13. Wood J, Rogers E, Owens H (1998) A formal theory of matrix primeness. Math. Control Signals Syst 11:40-78
14. Weiner PA (1998) Multidimensional convulutional codes. PhD Thesis, Mathematics Deparment, Notre Dame University
15. Wang M, Kwong CP (2002) Compute GCLF using syzygy algorithm. In: Cohen AM et al (eds) Proceedings of the first international congress of mathematical software, World Scientific, Singapore, pp 93-103
16. Youla DC, Gnavi G (1979) Notes on n -dimensional system theory. IEEE Trans Circuits Syst 26(2):105-111
17. Youla DC, Pickel PF (1984) The Quillen-Suslin theorem and the structure of n-dimensional elementary polynomial matrices. IEEE Trans Circuits Syst 31(6):513-518
18. Zerz E (2000) Coprime factorizations of multivariate rational matrices. Math. Control Signals Syst 13(2):125-139