Geodesic
Algebraic condition for decomposition of large-scale linear dynamic systems
International Journal of Applied Mathematics and Computer Science, Tome 19 (2009) no. 1, pp. 107-111.

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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.
Keywords: decomposition, algebraic condition, dynamic system
Mots-clés : rozkład, warunek algebraiczny, system dynamiczny 
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Górecki, H. Algebraic condition for decomposition of large-scale linear dynamic systems. International Journal of Applied Mathematics and Computer Science, Tome 19 (2009) no. 1, pp. 107-111. http://geodesic.mathdoc.fr/item/IJAMCS_2009_19_1_a9/

[1] Alagar, V. S. and Thanh, M. (1985). Fast polynomical decomposition algorithms, Lecture Notes in Computer Science 204: 150-153.

[2] Bartoni, D. R. and Zippel, R. (1985). Polynomial decomposition algorthims, Journal of Symbolic Computations 1(2): 159-168.

[3] 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.

[4] 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.

[5] 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.

[6] Gathen, J. (1990). Functional decomposition of polynomials: The tame case, Journal of Symbolic Computations 9: 281-299.

[7] 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.

[8] Górecki, H. and Popek, L. (1987). Algebraic condition for decomposition of large-scale linear dynamic systems, Automatyka 42: 13-28.

[9] Kozen, D. and Landau, S. (1989). Polynomial decomposition algorithms, Journal of Symbolic Computations 22: 445-456.

[10] Kozen, D., Landau, S. and Zippel, R.(1996). Decomposition of algebraic functions, Journal of Symbolic Computations 22: 235-246.

[11] Mostowski, A. and Stark, M. (1954). Advanced Algebra, Polish Scientific Publishers, Warsaw, (in Polish).

[12] Perron, O. (1927). Algebra, Walter de Gruyter and Co, Berlin, (in German).

[13] Suszkiewicz, A. (1941). Fundamentals of Advanced Algebra, OGIZ, Moscow, (in Russian).

[14] 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.