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Article

Fischer, Cyril ; Náprstek, Jiří
Remarks on inverse of matrix polynomials. (English). In: Chleboun, J., Kůs, P., Přikryl, P., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Janov nad Nisou, June 19-24, 2016. Institute of Mathematics CAS, Prague, 2017. pp. 24-29
MSC: 15A15, 15A18, 30C10, 34M03, 65H10 | DOI: 10.21136/panm.2016.03
Keywords:
matrix polynomial; polynomial eigenvalues; structural vibration
Summary:
Analysis of a non-classically damped engineering structure, which is subjected to an external excitation, leads to the solution of a system of second order ordinary differential equations. Although there exists a large variety of powerful numerical methods to accomplish this task, in some cases it is convenient to formulate the explicit inversion of the respective quadratic fundamental system. The presented contribution uses and extends concepts in matrix polynomial theory and proposes an implementation of the inversion problem.
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