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Numerical Methods in Discrete Inverse Problems
Kubínová, Marie ; Hnětynková, Iveta (advisor) ; Gazzola, Silvia (referee) ; Meurant, Gerard (referee)
Title: Numerical Methods in Discrete Inverse Problems Author: Marie Kubínová Department: Department of Numerical Mathematics Supervisor: RNDr. Iveta Hnětynková, Ph.D., Department of Numerical Mathe- matics Abstract: Inverse problems represent a broad class of problems of reconstruct- ing unknown quantities from measured data. A common characteristic of these problems is high sensitivity of the solution to perturbations in the data. The aim of numerical methods is to approximate the solution in a computationally efficient way while suppressing the influence of inaccuracies in the data, referred to as noise, that are always present. Properties of noise and its behavior in reg- ularization methods play crucial role in the design and analysis of the methods. The thesis focuses on several aspects of solution of discrete inverse problems, in particular: on propagation of noise in iterative methods and its representation in the corresponding residuals, including the study of influence of finite-precision computation, on estimating the noise level, and on solving problems with data polluted with noise coming from various sources. Keywords: discrete inverse problems, iterative solvers, noise estimation, mixed noise, finite-precision arithmetic - iii -
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"Kangaroo" and the system of care of childern requiring immediate assistance
Strnadová, Hana ; Pazlarová, Hana (advisor) ; Kubínová, Marie (referee)
Subject of this bachelor work are children in difficult situations and in demand of direct help or if you like fund threatend children Kangaroo, witch offer immediate family care solution. Purpose of this work was to find out, who are children who need immediate help. Than evaluate what kind of service kangaroo specify, and what kind of service provide in reality. The children who fall into kangaroo have in most cases syndrome CAN. In this case we talking about abuse and neglected children. In next case are children witch for some reason there parents can't take care of them. The legislative framework of this issue is stipulated in section 42 of act 359/1999 collection, on the social protection of children as amended. In particular therein before skilled description segments. I draw from technical literature. In valuation given services I gather mostly from my own experiences in specific kangaroo and materials FOD. In comparison I find out a difference between kangaroo and other foster care institution. Kangaroo is special in offering fast family care. Children being in a group mostly in four have constantly two ,,aunts" taking care of them switching by week witch should simulate family care. However taking into account the capacity of building, kids similar as in other institutions live in band of about 40...
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The Implementation of a School Education Programme in a Primary School with a view to Education in the Field of Mathematics and its Application
Žišková, Hana ; Kubínová, Marie (advisor) ; Sýkora, Václav (referee)
The main part of this thesis is disquisition dealing with the implementing of the Frame education programme for elementary school especially in the field of education considering Mathematics and its application in the Orlickoustecko region. The thesis is focused mainly onto the teachers and their problems with school education programme elaboration. Inevitable parts of disquisition are also analysis of the region and particular schools in term of uprise conditions of such an education programme, questionnaire disquisition and its interpretation, subsequent interviews with teachers and last but not least the case study of school education programmes for lower classes of multi-annual grammar schools chiefly in the field of education considering Mathematics and its application. The first part brings in starting points, which implicate the elaboration and subsequent interpretation of the disquisition. It is mainly about historical connections and about status quo and modern trends analyses in the field of education considering Mathematics. It also draws near the project and constructive teaching in Mathematics. One of the pillar starting points is also background and literature research (including Frame education programme for elementary school) focused onto the education considering v Mathematics and its...
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Regularization techniques based on the least squares method
Kubínová, Marie ; Hnětynková, Iveta (advisor)
Title: Regularization Techniques Based on the Least Squares Method Author: Marie Michenková Department: Department of Numerical Mathematics Supervisor: RNDr. Iveta Hnětynková, Ph.D. Abstract: In this thesis we consider a linear inverse problem Ax ≈ b, where A is a linear operator with smoothing property and b represents an observation vector polluted by unknown noise. It was shown in [Hnětynková, Plešinger, Strakoš, 2009] that high-frequency noise reveals during the Golub-Kahan iterative bidiagonalization in the left bidiagonalization vectors. We propose a method that identifies the iteration with maximal noise revealing and reduces a portion of high-frequency noise in the data by subtracting the corresponding (properly scaled) left bidiagonalization vector from b. This method is tested for different types of noise. Further, Hnětynková, Plešinger, and Strakoš provided an estimator of the noise level in the data. We propose a modification of this estimator based on the knowledge of the point of noise revealing. Keywords: ill-posed problems, regularization, Golub-Kahan iterative bidiagonalization, noise revealing, noise estimate, denoising 1
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Numerical Methods in Discrete Inverse Problems
Kubínová, Marie ; Hnětynková, Iveta (advisor) ; Gazzola, Silvia (referee) ; Meurant, Gerard (referee)
Title: Numerical Methods in Discrete Inverse Problems Author: Marie Kubínová Department: Department of Numerical Mathematics Supervisor: RNDr. Iveta Hnětynková, Ph.D., Department of Numerical Mathe- matics Abstract: Inverse problems represent a broad class of problems of reconstruct- ing unknown quantities from measured data. A common characteristic of these problems is high sensitivity of the solution to perturbations in the data. The aim of numerical methods is to approximate the solution in a computationally efficient way while suppressing the influence of inaccuracies in the data, referred to as noise, that are always present. Properties of noise and its behavior in reg- ularization methods play crucial role in the design and analysis of the methods. The thesis focuses on several aspects of solution of discrete inverse problems, in particular: on propagation of noise in iterative methods and its representation in the corresponding residuals, including the study of influence of finite-precision computation, on estimating the noise level, and on solving problems with data polluted with noise coming from various sources. Keywords: discrete inverse problems, iterative solvers, noise estimation, mixed noise, finite-precision arithmetic - iii -
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Regularization techniques based on the least squares method
Kubínová, Marie ; Hnětynková, Iveta (advisor)
Title: Regularization Techniques Based on the Least Squares Method Author: Marie Michenková Department: Department of Numerical Mathematics Supervisor: RNDr. Iveta Hnětynková, Ph.D. Abstract: In this thesis we consider a linear inverse problem Ax ≈ b, where A is a linear operator with smoothing property and b represents an observation vector polluted by unknown noise. It was shown in [Hnětynková, Plešinger, Strakoš, 2009] that high-frequency noise reveals during the Golub-Kahan iterative bidiagonalization in the left bidiagonalization vectors. We propose a method that identifies the iteration with maximal noise revealing and reduces a portion of high-frequency noise in the data by subtracting the corresponding (properly scaled) left bidiagonalization vector from b. This method is tested for different types of noise. Further, Hnětynková, Plešinger, and Strakoš provided an estimator of the noise level in the data. We propose a modification of this estimator based on the knowledge of the point of noise revealing. Keywords: ill-posed problems, regularization, Golub-Kahan iterative bidiagonalization, noise revealing, noise estimate, denoising 1
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The Implementation of a School Education Programme in a Primary School with a view to Education in the Field of Mathematics and its Application
Žišková, Hana ; Kubínová, Marie (advisor) ; Sýkora, Václav (referee)
The main part of this thesis is disquisition dealing with the implementing of the Frame education programme for elementary school especially in the field of education considering Mathematics and its application in the Orlickoustecko region. The thesis is focused mainly onto the teachers and their problems with school education programme elaboration. Inevitable parts of disquisition are also analysis of the region and particular schools in term of uprise conditions of such an education programme, questionnaire disquisition and its interpretation, subsequent interviews with teachers and last but not least the case study of school education programmes for lower classes of multi-annual grammar schools chiefly in the field of education considering Mathematics and its application. The first part brings in starting points, which implicate the elaboration and subsequent interpretation of the disquisition. It is mainly about historical connections and about status quo and modern trends analyses in the field of education considering Mathematics. It also draws near the project and constructive teaching in Mathematics. One of the pillar starting points is also background and literature research (including Frame education programme for elementary school) focused onto the education considering v Mathematics and its...
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Using Projects to Motivate Students in Mathematics
Složilová, Šárka ; Kubínová, Marie (advisor) ; Dvořák, Petr (referee)
This diploma thesis aims to show the possible use of project teaching in order to motivate pupils to study mathematics. The thesis is interspersed with author's self-reflections which came up during her study of motivation questions, project teaching and above all, the construction of projects. The content is divided into five parts. The first of them follows the author's motivation to write this thesis. Second chapter is theoretical; it is concerned with the psychological and didactical point of view on pupils' motivation to study. Third chapter deals with projects. In this chapter, a development of the project method is described, the basic notions are defined, the applicability of projects is analysed from the point of view of new approaches to motivate pupils and the project teaching is characterised as a specific educational theory. The fourth chapter contains a general description of planning and construction of projects in mathematics, an analysis of author's primary projects in comparison with her new knowledge and a new project creation detailed process. Fifth chapter gives information about the Czech education reforms, about the fundamental themes of RVP ZV (General educational programme for elementary school) and about the use of project teaching in school educational programmes. Powered by TCPDF...
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"Kangaroo" and the system of care of childern requiring immediate assistance
Strnadová, Hana ; Pazlarová, Hana (advisor) ; Kubínová, Marie (referee)
Subject of this bachelor work are children in difficult situations and in demand of direct help or if you like fund threatend children Kangaroo, witch offer immediate family care solution. Purpose of this work was to find out, who are children who need immediate help. Than evaluate what kind of service kangaroo specify, and what kind of service provide in reality. The children who fall into kangaroo have in most cases syndrome CAN. In this case we talking about abuse and neglected children. In next case are children witch for some reason there parents can't take care of them. The legislative framework of this issue is stipulated in section 42 of act 359/1999 collection, on the social protection of children as amended. In particular therein before skilled description segments. I draw from technical literature. In valuation given services I gather mostly from my own experiences in specific kangaroo and materials FOD. In comparison I find out a difference between kangaroo and other foster care institution. Kangaroo is special in offering fast family care. Children being in a group mostly in four have constantly two ,,aunts" taking care of them switching by week witch should simulate family care. However taking into account the capacity of building, kids similar as in other institutions live in band of about 40...
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