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Effective Algorithms for High-Precision Computation of Elementary Functions
Chaloupka, Jan ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
Nowadays high-precision computations are still more desired. Either for simulation on a level of atoms where every digit is important and inaccurary in computation can cause invalid result or numerical approximations in partial differential equations solving where a small deviation causes a result to be useless. The computations are carried over data types with precision of order hundred to thousand digits, or even more. This creates pressure on time complexity of problem solving and so it is essential to find very efficient methods for computation. Every complex physical problem is usually described by a system of equations frequently containing elementary functions like sinus, cosines or exponentials. The aim of the work is to design and implement methods that for a given precision, arbitrary elementary function and a point compute its value in the most efficent way. The core of the work is an application of methods based on AGM (arithmetic-geometric mean) with a time complexity of order $O(M(n)\log_2{n})$ 9(expresed for multiplication $M(n)$). The complexity can not be improved. There are many libraries supporting multi-precision atithmetic, one of which is GMP and is about to be used for efficent method implementation. In the end all implemented methods are compared with existing ones.
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Meta-learning methods for analyzing Go playing trends
Moudřík, Josef ; Neruda, Roman (advisor) ; Mráz, František (referee)
This thesis extends the methodology for extracting evaluations of players from samples of Go game records originally presented in (Baudiš - Moudřík, 2012). Firstly, this work adds more features and lays out a methodology for their comparison. Secondly, we develop a robust machine-learning framework, which is able to capture dependencies between the evaluations and general target variable using ensemble meta-learning with a genetic algorithm. We apply this framework to two domains, estimation of strength and styles. The results show that the inference of the target variables in both cases is viable and reasonably precise. Finally, we present a web application, which realizes the methodology, while presenting a prototype teaching aid for the Go players and gathering more data. Powered by TCPDF (www.tcpdf.org)
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Effective Algorithms for High-Precision Computation of Elementary Functions
Chaloupka, Jan ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
Nowadays high-precision computations are still more desired. Either for simulation on a level of atoms where every digit is important and inaccurary in computation can cause invalid result or numerical approximations in partial differential equations solving where a small deviation causes a result to be useless. The computations are carried over data types with precision of order hundred to thousand digits, or even more. This creates pressure on time complexity of problem solving and so it is essential to find very efficient methods for computation. Every complex physical problem is usually described by a system of equations frequently containing elementary functions like sinus, cosines or exponentials. The aim of the work is to design and implement methods that for a given precision, arbitrary elementary function and a point compute its value in the most efficent way. The core of the work is an application of methods based on AGM (arithmetic-geometric mean) with a time complexity of order $O(M(n)\log_2{n})$ 9(expresed for multiplication $M(n)$). The complexity can not be improved. There are many libraries supporting multi-precision atithmetic, one of which is GMP and is about to be used for efficent method implementation. In the end all implemented methods are compared with existing ones.
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Učení vícevrstvých perceptronů s po částech lineárními aktivačními funkcemi
Kozub, P. ; Holeňa, Martin
This paper presents an overview of the techniques used to solve constrained optimization problems using evolutionary algorithms. The construction of the fitness function together with the handling of feasible and infeasible individuals is discussed. Approaches using penalty functions, special representations, repair algorithms, methods based on separation of objective and constraints and multiobjective techniques are mentioned.
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Implicitní aproximace Bellmanovy rovnice
Pištěk, Miroslav
In this article, an efficient algorithm for an optimal decision strategy approximation is introduced. It approximate the Bellman equation without omitting the principial uncertainty stemming from an uncomplete knowledge. An integral part of the proposed solution is a reduction of memory demands using HDMR approximation. The result of this method is a linear algebraic system for an approximated upper bound on the Bellman function. One illustrative example has been completely resolved.
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