| Title:
|
An extension of the root perturbation $m$-dimensional polynomial factorization method (English) |
| Author:
|
Mastorakis, Nikos E. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
32 |
| Issue:
|
5 |
| Year:
|
1996 |
| Pages:
|
443-453 |
| . |
| Category:
|
math |
| . |
| MSC:
|
12Y05 |
| MSC:
|
26C10 |
| MSC:
|
65H05 |
| MSC:
|
65H10 |
| MSC:
|
93B40 |
| MSC:
|
93B60 |
| idZBL:
|
Zbl 0886.65053 |
| idMR:
|
MR1420134 |
| . |
| Date available:
|
2009-09-24T19:04:12Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/124822 |
| . |
| Reference:
|
[1] A. C. Antulas: A system-theoretic approach to the factorization theory of non-singular polynomial matrices.Internat. J. Systems Sci. 33 (1981), 6, 1005-1026. MR 0624168 |
| Reference:
|
[2] J. S. Chakrabarti, S. K. Mitra: An algorithm for multivariable polynomial factorization.In: Proc. IEEE Internat. Symp. Circ. Syst. 1977, pp. 678-683. |
| Reference:
|
[3] G. E. Collins: Computer algebra of polynomials and functions.Amer. Math. Monthly 80 (1973), 725-755. MR 0323750 |
| Reference:
|
[4] D. E. Dudgeon: The existence of cepstra for 2-D polynomials.IEEE Trans. Acoust. Speech Signal Process. ASSP-23 (1975), 2, 242-243. |
| Reference:
|
[5] M. P. Ekstrom, R. E. Twogood: Finite order, recursive models for 2-D random fields.In: Proc. of the 20th Hidwest Symp. Circ. Syst. 1977, pp. 188-189. |
| Reference:
|
[6] M. P. Ekstrom, J. W. Woods: Spectral factorization.IEEE Trans. Acoust. Speech Signal Process. ASSP-24 (1976), 2, 115-128. MR 0398676 |
| Reference:
|
[7] R. Gorez: Matrix factorization. Chandrasekhar equations techniques in the design of linear quadratic optimal control systems.Internat. J. Systems Sci. 12 (1981), 8, 907-915. MR 0628077 |
| Reference:
|
[8] R. L. Graham D. E. Knuth, O. Patashnik: Concrete Mathematics, A Foundation for Computer Science.Addison-Wesley Publishing Company, New York 1994. MR 1397498 |
| Reference:
|
[9] T. Kaczorek: Two-Dimensional Linear Systems.Springer-Verlag, Berlin--Heidelberg 1985. Zbl 0593.93031, MR 0870854 |
| Reference:
|
[10] D. E. Knuth: The Art of Computer Programming. Vol. 1: Fundamental algorithms. -- Vol. 2: Seminumerical Algorithms. -- Vol. 3: Electronic Digital Computers -- Programming.Addison-Wesley Publishing Company, London--Amsterdam--Ontario--Sydney 1981. MR 0378456 |
| Reference:
|
[11] N. E. Mastorakis: Multidimensional Polynomials.Ph.D. Thesis. National Technical University of Athens 1992. Zbl 0781.93048 |
| Reference:
|
[12] N. E. Mastorakis, E. Nikos: Algebra and Analysis of Multivariable Polynomials: General methods of multivariable polynomial factorization.Athens 1988. (In Greek). |
| Reference:
|
[13] N. E. Mastorakis, N. J. Theodorou: 'Operators' method for $m$-D polynomials factorization.Found. Comput. Decision Sci. 15 (1990), 2-3, 159-172. MR 1114659 |
| Reference:
|
[14] N. E. Mastorakis S. G. Tzafestas, N. J. Theodorou: A simple multidimensional polynomial factorization method.In: IMACS-IFAC Internat. Symp. on Math. and Intelligent Models in System Simulation, Brussels 1990, VII.B.1-1. |
| Reference:
|
[15] N. E. Mastorakis, N. J. Theodorou: State-space model factorization in $m$-dimensions. Application in stability.Foundation of Computing and Decision Sciences 17 (1992), 55-61. MR 1174151 |
| Reference:
|
[16] N. E. Mastorakis N. J. Theodorou, S. G. Tzafestas: Factorization of $m$-D polynomials into linear $m$-D factors.Internat. J. Systems Sci. 23 (1992), 11, 1805-1824. MR 1194285 |
| Reference:
|
[17] N. E. Mastorakis N. J. Theodorou, S. G. Tzafestas: A general factorization method for multivariable polynomial.Mult. Syst. and Sign. Process. 5 (1994), 151-178. MR 1279541 |
| Reference:
|
[18] N. E. Mastorakis S. G. Tzafestas, N. J. Theodorou: A reduction method for multivariable polynomial factorization.In: Conference SPRANN'94, IMACS-IEEE International Symposium, Lille 1994, pp. 59-64. |
| Reference:
|
[19] N. E. Mastorakis S. G. Tzafestas, N. J. Theodorou: Multidimensional polynomial factorization through the root perturbation approach. Part I.Control Theory Adv. Technology 10 (1994), 4, 901-911. MR 1330954 |
| Reference:
|
[20] P. Misra, R. V. Patel: Simple factorizability of 2-D polynomials.In: Internat. Symp. Circ. Syst., New Orleans 1990, pp. 1207-1210. |
| Reference:
|
[21] L. S. Shieh, N. Clahin: A computer-aided method for the factorization of matrix polynomials.Internat. J. Systems Sci. 12 (1981), 3, 305-323. MR 0610912 |
| Reference:
|
[22] N. J. Theodorou, S. C. Tzafestas: Factorizability conditions for multidimensional polynomials.IEEE Trans. Automat. Control AC-30 (1985), 7, 697-700. Zbl 0563.12019, MR 0790261 |
| Reference:
|
[23] S. G. Tzafestas (ed.): Multidimensional Systems. Techniques and Applications.Marcel Dekker, New York 1986. Zbl 0624.00025 |
| Reference:
|
[24] P. W. Wang, L. P. Rotchild: Factorizing over the integers.Comput. Math. 30 (1975), 324-336. |
| . |
