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Your search keyword '"Kopal, Jiří"' showing total 12 results
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12 results on '"Kopal, Jiří"'

1. Localising the Smallest Stiffness and its Direction of a Homogeneous Structure by Spectral and Optimisation Approaches

Author

Henyš, Petr, Sutula, Danas, Kopal, Jiří, Kuchař, Michal, and Čapek, Lukáš

Subjects
Condensed Matter - Mesoscale and Nanoscale Physics, Condensed Matter - Materials Science
Abstract

Structural stiffness plays an important role in engineering design. The analysis of stiffness requires precise experiments and computational models that can be difficult or time-consuming to procure. A novel relation between modal and static stiffness based on modal decomposition is introduced in this study. This relation allows analysing the smallest structural stiffness and its direction. Further, it is shown that the smallest stiffness can be found using an optimisation algorithm that is based on the maximisation of structural compliance. Both approaches are compared on several computational examples leading to similar results in terms of smallest stiffness and its direction. The proposed approaches serve as quantitative/qualitative tools for the analyses of structural stiffness, particularly in structural health monitoring., Comment: 28 pages, 13 figures

Published
2020

4. A note on adaptivity in factorized approximate inverse preconditioning

Author

Kopal Jiří, Rozložník Miroslav, and Tůma Miroslav

Subjects
sparse approximate inverse preconditioners, approximate factorization, generalized gram-schmidt process, 15a23, 65e50, 65f05, 65f25, Mathematics, QA1-939
Abstract

The problem of solving large-scale systems of linear algebraic equations arises in a wide range of applications. In many cases the preconditioned iterative method is a method of choice. This paper deals with the approximate inverse preconditioning AINV/SAINV based on the incomplete generalized Gram–Schmidt process. This type of the approximate inverse preconditioning has been repeatedly used for matrix diagonalization in computation of electronic structures but approximating inverses is of an interest in parallel computations in general. Our approach uses adaptive dropping of the matrix entries with the control based on the computed intermediate quantities. Strategy has been introduced as a way to solve di cult application problems and it is motivated by recent theoretical results on the loss of orthogonality in the generalized Gram– Schmidt process. Nevertheless, there are more aspects of the approach that need to be better understood. The diagonal pivoting based on a rough estimation of condition numbers of leading principal submatrices can sometimes provide inefficient preconditioners. This short study proposes another type of pivoting, namely the pivoting that exploits incremental condition estimation based on monitoring both direct and inverse factors of the approximate factorization. Such pivoting remains rather cheap and it can provide in many cases more reliable preconditioner. Numerical examples from real-world problems, small enough to enable a full analysis, are used to illustrate the potential gains of the new approach.

Published
2020
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11. Comparison of least squares methods for problems with errors in the model

Author

Dvořák, Jan, Hnětynková, Iveta, and Kopal, Jiří

Subjects
fitování dat, singular value decomposition, metody nejmenších čtverců, singulární rozklad, data fitting, errors in the model, least squares methods, chyby v modelu
Abstract

In this work we study the least squares and the total least squares problem for the solution of linear aproximation problems. We introduce both formulations and we discuss the existence and uniqueness of their solutions. We show selected computational methods based on the singular value decomposition. Further we focus on algebraic relations between both solutions and associated residuals. We present several estimates for the norm of the difference between the least squares and total least squares solution. We discuss their dependance on singular values of A and ( A b ) . Finally we illustrate the methods on selected test problems in the Matlab enviroment. 1

Published
2019

12. Aplikace výpočetních metod v třídění skleněných kamenů

Author

Lébl, Matěj, Hnětynková, Iveta, and Kopal, Jiří

Subjects
detekce objektů, digital image processing, convolution, thresholding, konvoluce, object detection, zpracování digitálního obrazu, prahování
Abstract

Application of computational methods in classification of glass stones Bc. Matěj Lébl Abstrakt: The goal of this thesis is to employ mathematical image processing methods in automatic quality control of glass jewellery stones. The main math- ematical subject is a matrix of specific attributes representing digital image of the studied products. First, the thesis summarizes mathematical definition of digital image and some standard image processing methods. Then, a complete solution to the considered problem is presented. The solution consists of stone localization within the image followed by analysis of the localized area. Two lo- calization approaches are presented. The first is based on the matrix convolution and optimized through the Fourier transform. The second uses mathematical methods of thresholding and median filtering, and data projection into one di- mension. The localized area is analyzed based on statistical distribution of the stone brightness. All methods are implemented in the MATLAB environment. 1

Published
2019

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