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National Repository of Grey Literature

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	Numerical range of an interval matrix Ivičič, Michal ; Hladík, Milan (advisor) ; Tichý, Petr (referee) The numerical range of a matrix is a set of complex numbers that contains all the eigen- values of the matrix. It is used for instance to estimate a matrix norm. This thesis is about the numerical range of an interval matrix. In the theoretical part, we examine its properties. We prove for example that it is NP-hard to find out whether a given point lies in the numerical range. On an example, we show that field of values of an interval matrix is not necessarily convex. The thesis contains descriptions of two algorithms for visualization of the convex hull of the numerical range. Both of them are only suitable for matrices of small sizes due to high time complexity. Therefore we also present a polyno- mial algorithm for computing the upper bound of the numerical range. In the practical part, we implement the algorithms as functions in the Matlab language. 1 Detailed record
	Rayleigh´s field in dynamics Kozánek, Jan ; Scopel, D. The method of analysis of the mathematical models of non-conservative and non-symmetric dynamic systems is presented. We seek a global insight into dynamic properties of the investigated system with help of the Rayleigh's Field of Values in complex plane. Detailed record
	Numerický obor a numerický poloměr Žitný, K. ; Kozánek, Jan Numerical range and numerical radius as an important instrument for the description of linear operators are analysed in this paper. The possibilities of the computations of the numerical range and numerical radius are presented, too. Detailed record

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