Graphes et algorithme de calcul de probabilités stationnaires d'un processus markovien discret
Graphical models provide an undirected graph representation of relations between the components of a random vector. In the Gaussian case such an undirected graph is used to describe conditional independence relations among such components. In this paper, we consider a continuous-time Gaussian model which is accessible to observations only at time . We introduce the concept of infinitesimal conditional independence for such a model. Then, we address the corresponding graphical model selection problem,...
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...
The paper presents the solution to the geodetic boundary value problem by the finite element method in area of Slovak Republic. Generally, we have made two numerical experiments. In the first one, Neumann BC in the form of gravity disturbances generated from EGM-96 is used and the solution is verified by the quasigeoidal heights generated directly from EGM-96. In the second one, Neumann BC is computed from gravity measurements and the solution is compared to the quasigeoidal heights obtained by...
This paper addresses a combinatorial optimization problem (COP), namely a variant of the (standard) matrix chain product (MCP) problem where the matrices are square and either dense (i.e. full) or lower/upper triangular. Given a matrix chain of length n, we first present a dynamic programming algorithm (DPA) adapted from the well known standard algorithm and having the same O(n3) complexity. We then design and analyse two optimal O(n) greedy algorithms leading in general to different optimal solutions...
This paper addresses a combinatorial optimization problem (COP), namely a variant of the (standard) matrix chain product (MCP) problem where the matrices are square and either dense (i.e. full) or lower/upper triangular. Given a matrix chain of length n, we first present a dynamic programming algorithm (DPA) adapted from the well known standard algorithm and having the same O(n3) complexity. We then design and analyse two optimal O(n) greedy algorithms leading in general to different optimal solutions...
Making use of a line integral defined without use of the partition of unity, Green’s theorem is proved in the case of two-dimensional domains with a Lipschitz-continuous boundary for functions belonging to the Sobolev spaces
The adjustment of one-dimensional space grid for a parabolic partial differential equation solved by the finite element method of lines is considered in the paper. In particular, the approach based on a posteriori error indicators and error estimators is studied. A statement on the rate of convergence of the approximation of error by estimator to the error in the case of a system of parabolic equations is presented.
Cet article décrit une approche de la modélisation d'un système d'acteurs, particulièrement adaptée à la modélisation des entreprises, fondée sur la théorie des jeux [11] et sur l'optimisation par apprentissage du comportement de ces acteurs. Cette méthode repose sur la combinaison de trois techniques : la simulation par échantillonnage (Monte-Carlo), la théorie des jeux pour ce qui concerne la recherche d'équilibre entre les stratégies, et les méthodes heuristiques d'optimisation locale,...
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 is employed for the upper bound. Several numerical experiments show applicability and accuracy of this approach.
We derive a posteriori error estimates for singularly perturbed reaction–diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable. Moreover, they are also locally efficient and robust in the sense that they represent local lower bounds for the actual error, up to a generic constant independent in particular of the reaction coefficient. We present our results in the framework of the vertex-centered finite volume method but their nature...
A method of characterizing all eigenvalues of a preconditioned discretized scalar diffusion operator with Dirichlet boundary conditions has been recently introduced in Gergelits, Mardal, Nielsen, and Strakoš (2019). Motivated by this paper, we offer a slightly different approach that extends the previous results in some directions. Namely, we provide bounds on all increasingly ordered eigenvalues of a general diffusion or elasticity operator with tensor data, discretized with the conforming finite...