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Newton and numerical mathematics
Obrátil, Štěpán ; Nechvátal, Luděk (referee) ; Zatočilová, Jitka (advisor)
Topic of this bachelor thesis are Newton's methods for numerical solutions of various problems. Especially the problems of solving nonlinear equations and systems of nonlinear equations, as well as numerical integration are explained. The Newton's method for solving nonlinear equations is presented, as well as its many modifications and its generalisation for systems of nonlinear equations. Usefulness of methods is demonstrated on various examples. In the end, Newton-Cotes quadrature formulae for numerical integration are presented.
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Conic optimization: theory and applications
Dortová, Zuzana ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
1 This work discusses the roles of second-order cone programming, these tasks are a special class semidefinitního programming. The work summarized basic de- finitions, properties and claims known about these tasks. Special attention is paid to methods of solving SOCP problems. In the last part of the paper are formu- lated in some special tasks of mathematical programming (linear programming, quadratic programming, ...) as special cases of SOCP problems.
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A tool for evaluation of different methods for solving nonlinear equations
Do Manh, Tuan ; Mikula, Tomáš (advisor) ; Horáček, Jaroslav (referee)
The objective of this work is to create a tool for solving nonlinear equations using numeric methods. It uses both slow working methods, such as bisection method or regula falsi method, and fast working methods, such as Newton's method. The Newton's method, while fast, can be very problematic in certain scenarios. It does not always converse to the root of the equation. That is why in this work, I try to implement modified methods, which attempt to deal with the imperfections of the Newton's method. The program is suppose to be a good tool for comparing and evaluating the efficiency of each methods in different situations.
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Newton and numerical mathematics
Obrátil, Štěpán ; Nechvátal, Luděk (referee) ; Zatočilová, Jitka (advisor)
Topic of this bachelor thesis are Newton's methods for numerical solutions of various problems. Especially the problems of solving nonlinear equations and systems of nonlinear equations, as well as numerical integration are explained. The Newton's method for solving nonlinear equations is presented, as well as its many modifications and its generalisation for systems of nonlinear equations. Usefulness of methods is demonstrated on various examples. In the end, Newton-Cotes quadrature formulae for numerical integration are presented.
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Conic optimization: theory and applications
Dortová, Zuzana ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
1 This work discusses the roles of second-order cone programming, these tasks are a special class semidefinitního programming. The work summarized basic de- finitions, properties and claims known about these tasks. Special attention is paid to methods of solving SOCP problems. In the last part of the paper are formu- lated in some special tasks of mathematical programming (linear programming, quadratic programming, ...) as special cases of SOCP problems.
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