The paper concerns the problem of decomposition of a large-scale linear dynamic system into two subsystems. An equivalent problem is to split the characteristic polynomial of the original system into two polynomials of lower degrees. Conditions are found concerning the coefficients of the original polynomial which must be fulfilled for its factorization. It is proved that knowledge of only one of the symmetric functions of those polynomials of lower degrees is sufficient for factorization of the characteristic polynomial of the original large-scale system. An algorithm for finding all the coefficients of the decomposed polynomials and a general condition of factorization are given. Examples of splitting the polynomials of the fifth and sixth degrees are discussed in detail.
@article{bwmeta1.element.bwnjournal-article-amcv19i1p107bwm,
author = {Henryk G\'orecki},
title = {Algebraic condition for decomposition of large-scale linear dynamic systems},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {19},
year = {2009},
pages = {107-111},
zbl = {1169.93304},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv19i1p107bwm}
}
Henryk Górecki. Algebraic condition for decomposition of large-scale linear dynamic systems. International Journal of Applied Mathematics and Computer Science, Tome 19 (2009) pp. 107-111. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv19i1p107bwm/
[000] Alagar, V. S. and Thanh, M. (1985). Fast polynomical decomposition algorithms, Lecture Notes in Computer Science 204: 150-153.
[001] Bartoni, D. R. and Zippel, R. (1985). Polynomial decomposition algorthims, Journal of Symbolic Computations 1(2): 159-168.
[002] Borodin, A., Fagin, R., Hopbroft, J. E. and Tompa, M. (1985). Decrasing the nesting depth of expressions involving square roots, Journal of Symbolic Computations 1(2): 169-188. | Zbl 0574.12001
[003] Coulter, R. S., Havas, G. and Henderson, M.(1998). Functional decomposition of a class of wild polynomials, Journal of Combinational Mathematics & Combinational Computations 28: 87-94. | Zbl 1067.11513
[004] Coulter, R. S., Havas, G. and Henderson, M. (2001). Giesbrecht's algorithm, the HFE cryptosystem and Ore's p8 polynomials, in K. Shirayangi and K. Yokoyama (Eds.), Lecture Notes Series of Computing, Vol. 9, World Scientific, Singapore, pp. 36-45. | Zbl 1018.12011
[005] Gathen, J. (1990). Functional decomposition of polynomials: The tame case, Journal of Symbolic Computations 9: 281-299. | Zbl 0716.68053
[006] Giesbrecht, M. and May, J. (2005). New algorithms for exact and approximate polynomial decomposition, Proceedings of the International Workshop on Symbolic-Numeric Computation, Xi'an, China, pp. 297-307.
[007] Górecki, H. and Popek, L. (1987). Algebraic condition for decomposition of large-scale linear dynamic systems, Automatyka 42: 13-28. | Zbl 0667.93005
[008] Kozen, D. and Landau, S. (1989). Polynomial decomposition algorithms, Journal of Symbolic Computations 22: 445-456. | Zbl 0691.68030
[009] Kozen, D., Landau, S. and Zippel, R.(1996). Decomposition of algebraic functions, Journal of Symbolic Computations 22: 235-246. | Zbl 0876.68062
[010] Mostowski, A. and Stark, M. (1954). Advanced Algebra, Polish Scientific Publishers, Warsaw, (in Polish). | Zbl 0057.01104
[011] Perron, O. (1927). Algebra, Walter de Gruyter and Co, Berlin, (in German). | Zbl 53.0081.10
[012] Suszkiewicz, A. (1941). Fundamentals of Advanced Algebra, OGIZ, Moscow, (in Russian).
[013] Watt, S. M. (2008). Functional decomposition of symbolic polynomials, Proceedings of the International Conference on Computational Science & Its Applications, Cracow, Poland, Vol. 5101, Springer, pp. 353-362.