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On the computation of the minimal polynomial of a polynomial matrix

100%
Karampetakis N. P., Tzekis P.
International Journal of Applied Mathematics and Computer Science
|
2005
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tom 15
|
nr 3
339-349
EN
The main contribution of this work is to provide two algorithms for the computation of the minimal polynomial of univariate polynomial matrices. The first algorithm is based on the solution of linear matrix equations while the second one employs DFT techniques. The whole theory is illustrated with examples.
2
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Infinite elementary divisor structure-preserving transformations for polynomial matrices

100%
Karampetakis N. P., Vologiannidis S.
International Journal of Applied Mathematics and Computer Science
|
2003
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tom 13
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nr 4
493-503
EN
The main purpose of this work is to propose new notions of equivalence between polynomial matrices that preserve both the finite and infinite elementary divisor structures. The approach we use is twofold: (a) the 'homogeneous polynomial matrix approach', where in place of the polynomial matrices we study their homogeneous polynomial matrix forms and use 2-D equivalence transformations in order to preserve their elementary divisor structure, and (b) the 'polynomial matrix approach', where some conditions between the 1-D polynomial matrices and their transforming matrices are proposed.
3
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On the computation of the GCD of 2-D polynomials

81%
Tzekis P., Karampetakis N. P., Terzidis H. K.
International Journal of Applied Mathematics and Computer Science
|
2007
|
tom 17
|
nr 4
463-470
EN
The main contribution of this work is to provide an algorithm for the computation of the GCD of 2-D polynomials, based on DFT techniques. The whole theory is implemented via illustrative examples.
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