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Guaranteed and fully computable two-sided bounds of Friedrichs' constant
Vejchodský, Tomáš
This contribution presents a general numerical method for computing lower and upper bound of the optimal constant in Friedrichs’ inequality. The standard Rayleigh-Ritz method is used for the lower bound and the method of a priori-a posteriori inequalities is employed for the upper bound. Several numerical experiments show applicability and accuracy of this approach.
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Smooth approximation of data with applications to interpolating and smoothings
Segeth, Karel
In the paper, we are concerned with some computational aspects of smooth approximation of data. This approach to approximation employs a (possibly infinite) linear combinations of smooth functions with coefficients obtained as the solution of a variational problem, where constraints represent the conditions of interpolating or smoothing. Some 1D numerical examples are presented.
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On selection of interface weights in domain decomposition methods
Čertíková, M. ; Šístek, Jakub ; Burda, P.
Different choices of the averaging operator within the BDDC method are compared on a series of 2D experiments. Subdomains with irregular interface and with jumps in material coefficients are included into the study. Two new approaches are studied along three standard choices. No approach is shown to be universally superior to others, and the resulting recommendation is that an actual method should be chosen based on properties of the problem.
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Massive parallel implementation of ODE solvers
Fischer, Cyril
The paper maps the possibilities of exploitation of the massive parallel computational hardware (namely GPU) for solution of the initial value problems of ordinary differential equations. Two cases are discussed: parallel solution of a single ODE and parallel execution of scalar ODE solvers. Whereas the advantages of the special architecture in the case of a single ODE are problematic, repeated solution of a single ODE for different data can prot from the parallel architecture. However, special algorithms have to be used even in the latter case to avoid code divergence be- tween individual computational threads. The topic is illustrated on several examples.
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Modifications of the limited-memory BFGS method based on the idea of conjugate directions
Vlček, Jan ; Lukšan, Ladislav
Simple modifications of the limited-memory BFGS method (L-BFGS) for large scale unconstrained optimization are considered, which consist in corrections of the used difference vectors (derived from the idea of conjugate directions), utilizing information from the preceding iteration. For quadratic objective functions, the improvement of convergence is the best one in some sense and all stored difference vectors are conjugate for unit stepsizes. The algorithm is globally convergent for convex sufficiently smooth functions. Numerical experiments indicate that the new method often improves the L-BFGS method significantly.
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Graphics card as a cheap supercomputer
Přikryl, Jan
The current powerful graphics cards, providing stunning real-time visual effects for computer-based entertainment, have to accommodate powerful hardware components that are able to deliver the photo-realistic simulation to the end-user. Given the vast computing power of the graphics hardware, its producers very often offer a programming interface that makes it possible to use the computational resources of the graphics processors (GPU) to more general purposes. This step gave birth to the so-called GPGPU (general-purpose GPU) processors that – if programmed correctly – are able to achieve astonishing performance in floating point operations. In this paper we will briefly overview nVidia CUDA technology and we will demonstrate a process of developing a simple GPGPU application both in the native GPGPU style and in the add-ons for Matlab (Jacket and Parallel Toolbox).
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