On computing determinants of large Sylvester type matrices
| Authors: | Kujan Petr, Czech Technical University, Faculty of Electrical Engineering, Czech Republic
Hromcik Martin, Czech Technical University, Faculty of Electrical Engineering, Centre for Applied Cybernetics, Czech Republic
Michael Sebek, Czech Technical University, Faculty of Electrical Engineering, Czech Republic |
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| Topic: | 2.1 Control Design |
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| Session: | Polynomial Design Methods: Applications |
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| Keywords: | Polynomial methods, Sylvester matrix, Resultant method, Numericalmethods, FFT, Determinant, Multilevel converter |
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Abstract
This work is devoted to computation of large n-D polynomial determinants with a special structure. Applications involve n-D systems theory (e.g. coprimeness test for two n-D polynomials) or the theory of algebraic equations. More specifically, these determinants were exploited by Chiasson recently to solve the practical problem of multilevel converter by a special computational procedure. To tackle the concerned problem it is essential to solve a system of polynomial equations with many unknowns. An algorithm was chosen based on elimination theory using resultants leading to the fundamental problem of computing determinants of large Sylvester type matrices with n-D polynomial entries. The aim of this work is to propose and test new numerical algorithms that would make it possible to solve the concerned problems more effectively.
