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Field of values of a matrix: Theory and computation
Vacek, Lukáš ; Tichý, Petr (advisor) ; Tůma, Miroslav (referee)
The field of values of a matrix A is a convex set in the complex plane assigned to A. It is important in matrix analysis, especially in invetigation of properties of nonnormal matrices and matrix polynomials, in study of the con- vergence of iterative methods applied to these matrices, in the estimation of ma- trix function norms, etc. This thesis summarizes theory about the field of values of a matrix, formulates open problems and explaines the main idea of the basic numerical method for its computation. In numerical experiments the standart algorithmic realization of method is compared with alternative approaches that use power method, Lanczos algorithm and Chebfun.
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MAT TRIAD 2019: Book of Abstracts
Bok, J. ; Hartman, David ; Hladík, M. ; Rozložník, Miroslav
This volume contains the Book of abstracts of the 8th International Conference on Matrix Analysis and its Applications, MAT TRIAD 2019. The MATTRIAD conferences represent a platform for researchers in a variety of aspects of matrix analysis and its interdisciplinary applications to meet and share interests and ideas. The conference topics include matrix and operator theory and computation, spectral problems, applications of linear algebra in statistics, statistical models, matrices and graphs as well as combinatorial matrix theory and others. The goal of this event is to encourage further growth of matrix analysis research including its possible extension to other fields and domains.
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Field of values of a matrix: Theory and computation
Vacek, Lukáš ; Tichý, Petr (advisor) ; Tůma, Miroslav (referee)
The field of values of a matrix A is a convex set in the complex plane assigned to A. It is important in matrix analysis, especially in invetigation of properties of nonnormal matrices and matrix polynomials, in study of the con- vergence of iterative methods applied to these matrices, in the estimation of ma- trix function norms, etc. This thesis summarizes theory about the field of values of a matrix, formulates open problems and explaines the main idea of the basic numerical method for its computation. In numerical experiments the standart algorithmic realization of method is compared with alternative approaches that use power method, Lanczos algorithm and Chebfun.
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