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Numerical comparison of the CGLS and LSQR algorithms
Mrňák, Petr ; Tichý, Petr (advisor) ; Tůma, Miroslav (referee)
This bachelor thesis deals with the introduction of two mathemati- cally equivalent algorithms, CGLS and LSQR, which can be viewed as versions of the method of conjugate gradients applied to a system of normal equations. This thesis is devoted to their comparison both from a theoretical point of view (showing the relations between vectors and coefficients) and from a practical point of view (the behaviour of both algorithms in finite precision arithmetic). 1
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Numerical comparison of the CGLS and LSQR algorithms
Mrňák, Petr ; Tichý, Petr (advisor) ; Tůma, Miroslav (referee)
This bachelor thesis deals with the introduction of two algorithms, namely LSQR and CGLS, and then their comparison in the field of theory and the field of practi- cal application and computation. First, it is important to lay the foundations for these algorithms by using conjugate gradients and Lanczos tridiagonalisation. Both algorithms are theoretically equivalent, but in practice it is necessary to distinguish between them which is more appropriate for a given calculation. 1
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Public authorities in the case law of the European Court of Justice
Mrňák, Petr ; Svátková, Slavomíra (advisor) ; Zídková, Hana (referee)
In my thesis I analyzed the characteristics of the legal concepts of bodies governed by public law and the activities in which they engage as public authorities, as used by law (both European and national) governing value added tax. I also analyzed the case law of the European Court of Justice relating to the issue of the bodies governed by public law and the activities in which they engage as public authorities in terms of value added tax. The characteristics of the concepts have been evaluated and sorted logically. In a separate part I examined the bodies governed by public law and their activities from an economic point of view. I have pondered whether it is necessary that these entities have a special position in the system of value added tax.
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