| Title:
|
Approximate stable multidimensional polynomial factorization into linear $m$-D polynomial factors (English) |
| Author:
|
Mastorakis, Nikos E. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
32 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
275-288 |
| . |
| Category:
|
math |
| . |
| MSC:
|
93B17 |
| MSC:
|
93B25 |
| MSC:
|
93C35 |
| idZBL:
|
Zbl 0880.93022 |
| idMR:
|
MR1438220 |
| . |
| Date available:
|
2009-09-24T19:02:40Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125517 |
| . |
| Reference:
|
[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. |
| Reference:
|
[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 0303723 |
| Reference:
|
[3] R. A. De Carlo J. Murray, R. Saeks: Multivariable Nyquist theory.Internat. J. Control 25 (1976), 5, 657-675. MR 0449829 |
| Reference:
|
[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 0604825 |
| Reference:
|
[5] T. Kaczorek: Two-Dimensional Linear Systems.Lecture Notes in Control and Inform. Sci. 68. Springer-Verlag, Berlin 1985. Zbl 0593.93031, MR 0870854 |
| Reference:
|
[6] K. Levenberg: A method for the solution of certain non-linear problems in least squares.Quart. Appl. Meth. 2 (1944), 164-168. Zbl 0063.03501, MR 0010666 |
| Reference:
|
[7] D. W. Marquardt: An algorithm for least-squares estimation of nonlinear parameters.SIAM J. 11 (1963), 2. Zbl 0112.10505, MR 0153071 |
| Reference:
|
[8] N. E. Mastorakis: Approximate and stable separable polynomial factorization.Found. Comput. Decision Sci. 21 (1996), 1, 55-64. Zbl 0861.93020, MR 1399859 |
| Reference:
|
[9] N. E. Mastorakis: Multidimensional Polynomials.PҺ.D. Thesis. National Technical University of Athens 1992. Zbl 0781.93048 |
| Reference:
|
[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 1114659 |
| Reference:
|
[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 0781.93048 |
| Reference:
|
[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. Zbl 0814.93036, MR 1174151 |
| Reference:
|
[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. |
| Reference:
|
[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. Zbl 0827.93036, MR 1319944 |
| Reference:
|
[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 1194285 |
| Reference:
|
[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. |
| Reference:
|
[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. |
| Reference:
|
[18] W. Murray (ed.): Numerical Methods for Unconstrained Optimization.Academic Press, New York 1972. |
| Reference:
|
[19] J. Murray: Another proof and shaгpening of Huang's theorem.IEEE Trans. Acoust. Speech Signal Process. ASSP-25 (1977), 581-582. |
| Reference:
|
[20] M. Powell: Problems Related to Unconstrained Optimization.Chapter in [18]. |
| Reference:
|
[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. |
| Reference:
|
[22] N. J. Theodorou, S. G. Tzafestas: Reducibility and factorizability of multivariable polynomials.Control Theory Adv. Tech. 1 (1985), 25-46. |
| Reference:
|
[23] S. G. Tzafestas (ed.): Multidimensional Systems: Techniques and Applications.Marcel Dekker, New York 1986. Zbl 0624.00025 |
| . |
