On factor prime factorizations for n-D polynomial matrices

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 54, Issue 6, 2007, Pages 1398-1405

  Wang, Mingsheng ^a  

^a INSTITUTE OF SOFTWARE   (China)

Author keywords

Factor prime matrix; Matrix factorization; Multidimensional systems; n D polynomial matrices; Polynomial ring

Indexed keywords

ALGORITHMS; MATRIX ALGEBRA; POLYNOMIALS;

FACTOR PRIME MATRIX; MATRIX FACTORIZATION; MULTIDIMENSIONAL SYSTEM; POLYNOMIAL MATRIX; POLYNOMIAL RING;

FACTORIZATION;

EID: 34250795617     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2007.897720     Document Type: Article

References (27)

1. N. K. Bose, B. Buchberger, and J. P. Guiver, Multidimensional Systems Theory and Applications. Dordrecht, The Netherlands: Kluwer, 2003.
2. C. Charoenlarpnopparut and N. K. Bose, "Multidimensional FIR filter bank design using Gröbner bases," IEEE Trans. Circuits Syst. II: Analog Digit. Signal Process., vol. 46, no. 12, pp. 1475-1486, Dec. 1999.
3. CoCoA: A System for Doing Computations in Commutative Algebra CoCoA Team Online. Available: http://cocoa.dima.unige.it
4. D. Eisenbud, Commutative Algebra With a View Towards Algebraic Geometry. New York: Springer, 1995.
5. E. Fornasini and M. E. Valcher, "n-D polynomial matrices with applications to multidimensional signal analysis," Multidim. Syst. Signal Process., vol. 8, pp. 387-408, 1997.
6. J. P. Guiver and N. K. Bose, "Polynomial matrix factorization over arbitrary coefficient field and related results," IEEE Trans. Circuits Syst., vol. CAS-29, no. 10, pp. 649-657, Oct. 1982.
7. G. M. Greuel and G. Pfister, A Singular Introduction to Commutative Algebra. Berlin: Springer, 2002.
8. G. M. Greuel, G. Pfister, and H. Schöneman, SINGULAR 3-0-1, A computer algebra system for polynomial computations. Center for computer algebra Univ. of Kaiserslautern, Kaiserslautern, Germany Online. Available: http://www.singular.uni-kl.de
9. M. Kreuzer and L. Robbiano, Computational Commutative Algebra I. Berlin, Germany: Springer-Verlag, 2000.
10. S. Kleon and U. Oberst, "Transfer operators and state spaces for discrete multidimensional linear systems," Act. Appl. Math., vol. 57, pp. 1-82, 1999.
11. Z. Lin, "On matrix fraction description of multivariable linear n-D systems," IEEE Trans. Circuits Syst., vol. 35, no. 10, pp. 1317-1322, Oct. 1988.
12. Z. Lin, "On primitive factorizations for 3-D polynomial matrices," IEEE Trans. Circuits Syst. vol. 39, no. 12, pp. 1024-1027, Dec. 1992.
13. Z. Lin, "Notes on n-D polynomial matrix factorization," Multidim. Syst. Signal Process., vol. 10, pp. 379-393, 1999.
14. Z. Lin and N. K. Bose, "A generalization of Serre's conjecture and related issues," Linear Algebra Appl., vol. 338, pp. 125-138, 2001.
15. Z. Lin, J. Q. Ying, and L. Xu, "Factorizations for n-D polynomial matrices," Circuits Syst. Signal Proces., vol. 20, pp. 601-618, 2001.
16. Z. Lin, L. Xu, and H. Fan, "On minor prime factorization for n-D polynomial matrices," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 52, no. 9, pp. 568-571, Sep. 2005.
17. T. Y. Lam, Serre's Problem on Projective Modules. Berlin, Germany: Springer-Verlag, 2006.
18. M. Morf, B. C. Levy, and S. Y. Kung, "New results in 2-D systems theory, part I: 2-D polynomial matrices, factorizations and coprimeness," Proc. IEEE vol. 65, no. 4, pp. 861-872, Apr. 1977.
19. J. F. Pommaret, "Solving Bose conjecture on linear multidimensional systems," in Proc. Eur. Control Conf., 2001, pp. 1853-1855.
20. H. Park, "Prime factorization of n-D polynomial matrices," in Proc. IEEE ISCAS, Bangkok, Thailand, May 2003 vol. III, pp. 666-669.
21. V. Srinivas, "A generalized Serre problem," J. Algebra vol. 278, no. 2, pp. 621-627, Aug. 2004.
22. J. Wood, E. Rogers, and H. Owens, "A formal theory of matrix primeness," Math. Contr. Signals Syst., vol. 11, pp. 40-78, 1998.
23. P. A.Weiner, "Multidimensional convulutional codes," Ph.D. dissertation, Math. Dep., Univ. of Notre Dame, South Bend, IN, 1998.
24. M.Wang and D. Feng, "On Lin-Bose problem," Linear Algebra Appl., vol. 390, pp. 279-285, Oct. 2004.
25. M. Wang and C. P. Kwong, "On multivariate polynomial matrix factorization problems," Math. Contr. Sign. Syst. vol. 17, no. 4, pp. 297-311, 2005.
26. D. C. Youla and G. Gnavi, "Notes on n-dimensional system theory," IEEE Trans. Circuits Syst. vol. CAS-26, no. 2, pp. 105-111, Feb. 1979.
27. D. C. Youla and P. F. Pickel, "The Quillen-Suslin theorem and the structure of n-dimensional elementary polynomial matrices," IEEE Trans. Circuits Syst., vol. CAS-31, no. 6, pp. 513-518, Jun. 1984.