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Orthogonal bases and their application in signal processing
Kárský, Vilém ; Tůma, Martin (referee) ; Jura, Pavel (advisor)
This work is concentrates on finding basic properties of some orthogonal polynomials like a definition, weight function, orthogonality interval, recurrence relations, number of zeros and diferential eguations which they were suited on. Subsequently were founded formulas for calculating coefficients of the generalized Fourir series and I concentrate on calculating optimal free parameters on this orthogonal polynomials. In the end of this work are calculated and displayed spectrums of some functions in the bases of individual polynomials and was calculated and displayed aproximation error.
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Methods of numerical integration
Čoupek, Filip ; Tomášek, Petr (referee) ; Zatočilová, Jitka (advisor)
This bachelor thesis focuses on numerical calculation of a simple specific integral. First, the basic concepts are established and briefly described interpolation and orthogonal polynomials, from which the individual formulas are based. Emphasis is placed on the introduction, derivation and description of Newton-Cotes quadrature formulas, Gauss quadrature formulas and Clenshaw-Curtis quadrature formulas. In the penultimate chapter we describe the principle of adaptive integration and Romberg's method. At the end of the thesis is a comparison of individual methods on specific examples using the software Matlab.
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Methods of numerical integration
Čoupek, Filip ; Tomášek, Petr (referee) ; Zatočilová, Jitka (advisor)
This bachelor thesis focuses on numerical calculation of a simple specific integral. First, the basic concepts are established and briefly described interpolation and orthogonal polynomials, from which the individual formulas are based. Emphasis is placed on the introduction, derivation and description of Newton-Cotes quadrature formulas, Gauss quadrature formulas and Clenshaw-Curtis quadrature formulas. In the penultimate chapter we describe the principle of adaptive integration and Romberg's method. At the end of the thesis is a comparison of individual methods on specific examples using the software Matlab.
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Analysis of the Stieltjes imaging method for the calculation of resonance widths
Votavová, Petra ; Kolorenč, Přemysl (advisor) ; Čížek, Martin (referee)
Title: Analysis of the Stieltjes imaging method for the calculation of resonance widths Author: Petra Votavová Department: Institute of Theoretical Physics Supervisor: RNDr. Přemysl Kolorenč, Ph.D., Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague Abstract: This thesis deals with the moment problem in the context of the resonance widths. The moment problem was solved by the Stieltjes imaging method and proposed alternative method based on the direct decomposition into the orthogonal basis. Three different basis derived from the Legendre polynomials were chosen. The properties of these methods were studied by analytical function. Eventually, both methods were applied to the calculation of resonance width of the metastable ion CH3F(2s-2 )2+ . Keywords: moment problem, Gaussian quadrature, orthogonal polynomials, resonance widths, decay of metastable ions
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Orthogonal bases and their application in signal processing
Kárský, Vilém ; Tůma, Martin (referee) ; Jura, Pavel (advisor)
This work is concentrates on finding basic properties of some orthogonal polynomials like a definition, weight function, orthogonality interval, recurrence relations, number of zeros and diferential eguations which they were suited on. Subsequently were founded formulas for calculating coefficients of the generalized Fourir series and I concentrate on calculating optimal free parameters on this orthogonal polynomials. In the end of this work are calculated and displayed spectrums of some functions in the bases of individual polynomials and was calculated and displayed aproximation error.
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