Approximate stable multidimensional polynomial factorization into linear $m$-D polynomial factors
Kybernetika, Tome 32 (1996) no. 3, pp. 275-288 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 93B17, 93B25, 93C35
@article{KYB_1996_32_3_a4,
     author = {Mastorakis, Nikos E.},
     title = {Approximate stable multidimensional polynomial factorization into linear $m${-D} polynomial factors},
     journal = {Kybernetika},
     pages = {275--288},
     year = {1996},
     volume = {32},
     number = {3},
     mrnumber = {1438220},
     zbl = {0880.93022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1996_32_3_a4/}
}
TY  - JOUR
AU  - Mastorakis, Nikos E.
TI  - Approximate stable multidimensional polynomial factorization into linear $m$-D polynomial factors
JO  - Kybernetika
PY  - 1996
SP  - 275
EP  - 288
VL  - 32
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/KYB_1996_32_3_a4/
LA  - en
ID  - KYB_1996_32_3_a4
ER  - 
%0 Journal Article
%A Mastorakis, Nikos E.
%T Approximate stable multidimensional polynomial factorization into linear $m$-D polynomial factors
%J Kybernetika
%D 1996
%P 275-288
%V 32
%N 3
%U http://geodesic.mathdoc.fr/item/KYB_1996_32_3_a4/
%G en
%F KYB_1996_32_3_a4
Mastorakis, Nikos E. Approximate stable multidimensional polynomial factorization into linear $m$-D polynomial factors. Kybernetika, Tome 32 (1996) no. 3, pp. 275-288. http://geodesic.mathdoc.fr/item/KYB_1996_32_3_a4/

[1] K. M. Brown: Computer Oriented Methods for Fitting Tabular Data in the Linear and Nonlinear Least Squares Sense. Research Report No. 72-13, Department of Computer, Information and Control Sciences, University of Minnesota 1972.

[2] K. M. Brown, J. E. Dennis: Derivative free analogues of the Levenberg-Marquardt and Gauss algorithms for nonlinear least squares approximations. Numer. Math. 18 (1972), 289-297. | MR

[3] R. A. De Carlo J. Murray, R. Saeks: Multivariable Nyquist theory. Internat. J. Control 25 (1976), 5, 657-675. | MR

[4] P. Delsarte Y. V. Genin, Y. G. Kamp: A simple proof of Rudin's multivariable stability theorem. IEEE Trans. Acoust. Speech Signal Process. ASSP-28 (1980), 6, 701-705. | MR

[5] T. Kaczorek: Two-Dimensional Linear Systems. Lecture Notes in Control and Inform. Sci. 68. Springer-Verlag, Berlin 1985. | MR | Zbl

[6] K. Levenberg: A method for the solution of certain non-linear problems in least squares. Quart. Appl. Meth. 2 (1944), 164-168. | MR | Zbl

[7] D. W. Marquardt: An algorithm for least-squares estimation of nonlinear parameters. SIAM J. 11 (1963), 2. | MR | Zbl

[8] N. E. Mastorakis: Approximate and stable separable polynomial factorization. Found. Comput. Decision Sci. 21 (1996), 1, 55-64. | MR | Zbl

[9] N. E. Mastorakis: Multidimensional Polynomials. PҺ.D. Thesis. National Technical University of Athens 1992. | Zbl

[10] N. E. Mastorakis, N. J. Theodorou: Operators' method for $m$-D polynomials factorization. Found. Comput. Decision Sci. 15 (1990), 3-4, 159-172. | MR

[11] N. E. Mastorakis, N. J. Theodorou: Approximate factorization of multidimensional polynomials depending on a parameter $\lambda$. Bull. Electronics of the Polish Academy 40 (1992), 1, 47-51. | Zbl

[12] N. E. Mastorakis, N. J. Theodorou: State-space model factorization in $m$-dimensions. Appl. in Stability. Found. Comput. Decision Sci. 17 (1992), 1, 55-61. | MR | Zbl

[13] N. E. Mastorakis, N. J. Theodorou: Simple, group and approximate factorization of multidimensional polynomials. In: IEEE-Mediterranean Conference on New Directions in Control Theory and Applications. Session: 2-D Systems, Chania 1993.

[14] N. E. Mastorakis, N. J. Theodorou: Exact and approximate multidimensional polynomial factorization. Application on measurement processing. Found. Comput. Decision Sci. 19 (1994), 4, 307-317. | MR | Zbl

[15] N. E. Mastorakis, N. J. Theodorou, S. G. Tzafestas: Multidimensional polynomial factorization in linear $m$-D factors. Internat. J. Systems Sci. 23 (1992), 11, 1805-1824. | MR

[16] 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, pp. VII.B.1-1.

[17] N. E. Mastorakis S. G. Tzafestas, N. J. Theodorou: A reduction method for multivariable polynomial factorization. In: International Symposium on Signal Processing, Robotics and Neural Networks (SPRANN-94), IMACS-IEEE. Proceedings Session 2-D Systems, Lille 1994.

[18] W. Murray (ed.): Numerical Methods for Unconstrained Optimization. Academic Press, New York 1972.

[19] J. Murray: Another proof and shaгpening of Huang's theorem. IEEE Trans. Acoust. Speech Signal Process. ASSP-25 (1977), 581-582.

[20] M. Powell: Problems Related to Unconstrained Optimization. Chapter in [18].

[21] J. L. Shanks S. Treital, J. H. Justice: Stability and synthesis of two dimensional recursive filters. IEEE Trans. Audio Electroacoust. 20 (1972), 115-208.

[22] N. J. Theodorou, S. G. Tzafestas: Reducibility and factorizability of multivariable polynomials. Control Theory Adv. Tech. 1 (1985), 25-46.

[23] S. G. Tzafestas (ed.): Multidimensional Systems: Techniques and Applications. Marcel Dekker, New York 1986. | Zbl