On the block decomposition and spectral factors of λ-matrices

• Autorzy: Bekhiti Belkacem , Nail Bachir , Dahimene Abdelhakim , Hariche Kamel , Fragulis George F.
• Języki publikacji: EN

Abstrakty

EN

In this paper we have factorized matrix polynomials into a complete set of spectral factors using a new design algorithm, and with some systematic procedures a complete set of block roots (solvents) have been obtained. The newly developed procedure is just an extension of the (scalar) Horner method to its block form for use in the computation of the block roots of matrix polynomial, the block-Horner method bringing a local iterative nature, faster convergence, nested programmable scheme, needless of any prior knowledge of the matrix polynomial, with the only one inconvenience, which is the strong dependence on the initial guess. In order to avoid this trap, we proposed a combination of two computational procedures, for which the complete program starts with the right block-Q.D. algorithm. It is then followed by a refinement of the right factor by block-Horner’s algorithm. This results in the global nature of the program, which is faster in execution, has well defined initial conditions, and good convergence in much less time.

Słowa kluczowe

EN

block roots; solvents; spectral factors; block-Q.D. algorithm; block-Horner’s algorithm; matrix polynomials

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2020
• Tom: Vol. 49, No. 1
• Strony: 41--76
• Opis fizyczny: Bibliogr. 42 poz., rys.

Twórcy

autor

Bekhiti Belkacem

• Institute of Aeronautics and Space Studies, Saad Dahlab University, Blida, Algeria

autor

Nail Bachir

• Mechanical Engineering, Materials and Structures Laboratory, Institute of Science and Technology, Tissemsilt University Center, Tissemsilt, Algeria

autor

Dahimene Abdelhakim

• Department of Control Systems, Electronics and Electrotechnics Institute, University of Boumerdes (Ex:INELEC), Algeria

autor

Hariche Kamel

• Department of Control Systems, Electronics and Electrotechnics Institute, University of Boumerdes (Ex:INELEC), Algeria

autor

Fragulis George F.

• Western Macedonia University of Applied Sciences, Kozani, Greece

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).