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	On a dynamics in rational polygonal billiards Soukenka, Martin For a special shaped rational polygonal billiard table we consider a dynamical system generated by the free motion of a mass-point subject to the elastic reflection in the boundary. By numerical experiments we study two open problems in the field: (i) an existence of so called Li-York chaos, (ii) maximal length of common itineraries in two quasi-similar rational polygons. Under detailed theoretical analysis and numerical results we postulate a conjecture. Detailed record
	On the worst scenario method: Application to uncertain nonlinear differential equations with numerical examples Harasim, Petr In this contribution, the worst scenario method is applied to problem described by nonlinear differential equation with uncertain coefficients. Above all, some illustrative numerical examples including algorithm are presented. Detailed record
	Integration in higher-order finite element method in 3D Kůs, Pavel Integration of higher-order basis functions is an important issue, that is not as straightforward as it may seem. In traditional low-order FEM codes, the bulk of computational time is a solution of resulting system of linear equations. In the case of higher-order elements the situation is different. Especially in three dimensions the time of integration may represent significant part of the computation. Detailed record
	Programs and Algorithms of Numerical Mathematics 15 Vejchodský, Tomáš ; Chleboun, J. ; Přikryl, Petr ; Segeth, Karel ; Šístek, Jakub The book contains papers presented at the international seminar Programs and algorithms of numerical Mathematics 15 (PANM 15), held in Dolni Maxov, Czech Republic, June 6-11, 2010. It is the fifteen volume in the series of the PANM proceedings. The topics of contributions include numerical methods for fluid flow modelling, the finite element method, a posteriori error estimates, topics from numerical linear atgebra, etc. Detailed record
	Complementarity - the way towards guaranteed error estimates Vejchodský, Tomáš This paper presents a review of the complementary technique with the emphasis on computable and guaranteed upper bounds of the approximation error. For simplicity, the approach is described on a numerical solution of the Poisson problem. We derive the complementary error bounds, prove their fundamentals properties, present the method of hypercircle, mention possible generalizations and show a couple of numerical examples. Detailed record
	Some remarks on averaging in the BDDC method Čertíková, M. ; Burda, P. ; Novotný, J. ; Šístek, Jakub In this paper, we introduce a general framework for derivation of the averaging operator, from hich the standard choices are recovered by simplifications. Then, an alternative approach derived by another simplification is proposed and tested on a 2D example. Detailed record
	A comparison of some a posteriori error estimates for fourth order problems Segeth, Karel In this survey contribution, we present and compare, from the viewpoint of adaptive computation, several recently published error estimation procedures for the numerical solution of biharmonic and some further fourth order problems including computational error estimates. Detailed record
	Limited-Memory Variable Metric Methods that use Quantities from the Preceding Iteration Vlček, Jan ; Lukšan, Ladislav In this contribution, a new family of globally convergent limited-memory (LM) variable metric (VM) line search methods for unconstrained minimization is presented. Numerical results indicate that the new methods can save computational time substantially for certain problems in comparison with the well-known L-BFGS method. Detailed record
	Robust Preconditioners for the Matrix Free Truncated Newton Method Lukšan, Ladislav ; Matonoha, Ctirad ; Vlček, Jan New positive definite preconditioners for the matrix free truncated Newton method are given. Corresponding algorithms are described in detail. Results of numerical experiments that confirm the efficiency and robustness of the preconditioned truncated Newton method are reported. Detailed record

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