Search results for "Approximations of π"
showing 10 items of 11 documents
On Extensional Fuzzy Sets Generated by Factoraggregation
2014
We develop the concept of a general factoraggregation operator introduced by the authors on the basis of an equivalence relation and applied in two recent papers for analysis of bilevel linear programming solving parameters. In the paper this concept is generalized by using a fuzzy equivalence relation instead of the crisp one. We show how the generalized factoraggregation can be used for construction of extensional fuzzy sets and consider approximations of arbitrary fuzzy sets by extensional ones.
Comparative Study of the a Posteriori Error Estimators for the Stokes Problem
2007
The research presented is focused on a comparative study of a posteriori error estimation methods to various approximations of the Stokes problem. Mainly, we are interested in the performance of functional type a posterior error estimates and their comparison with other methods. We show that functional type a posteriori error estimators are applicable to various types of approximations (including non-Galerkin ones) and robust with respect to the mesh structure, type of the finite element and computational procedure used. This allows the construction of effective mesh adaptation procedures in all cases considered. Numerical tests justify the approach suggested.
Reliable polygonal approximations of imaged real objects through dominant point detection
1998
Abstract The problem of dominant point detection is posed, taking into account what usually happens in practice. The algorithms found in the literature often prove their performance with laboratory contours, but the shapes in real images present noise, quantization, and high inter and intra-shape variability. These effects are analyzed and solutions to them are proposed. We will also focus on the conditions for an efficient (few points) and precise (low error) dominant point extraction that preserves the original shape. A measurement of the committed error (optimization error, E 0 ) that takes into account both aspects is defined for studying this feature.
A Characterization of Bispecial Sturmian Words
2012
A finite Sturmian word w over the alphabet {a,b} is left special (resp. right special) if aw and bw (resp. wa and wb) are both Sturmian words. A bispecial Sturmian word is a Sturmian word that is both left and right special. We show as a main result that bispecial Sturmian words are exactly the maximal internal factors of Christoffel words, that are words coding the digital approximations of segments in the Euclidean plane. This result is an extension of the known relation between central words and primitive Christoffel words. Our characterization allows us to give an enumerative formula for bispecial Sturmian words. We also investigate the minimal forbidden words for the set of Sturmian wo…
A Posteriori Error Bounds for Approximations of the Oseen Problem and Applications to the Uzawa Iteration Algorithm
2014
Abstract. We derive computable bounds of deviations from the exact solution of the stationary Oseen problem. They are applied to approximations generated by the Uzawa iteration method. Also, we derive an advanced form of the estimate, which takes into account approximation errors arising due to discretization of the boundary value problem, generated by the main step of the Uzawa method. Numerical tests confirm our theoretical results and show practical applicability of the estimates.
Splineapproximationen von beliebigem Defekt zur numerischen L�sung gew�hnlicher Differentialgleichungen. Teil III
1980
In the first part [5] a general procedure is presented to obtain polynomial spline approximations of arbitrary defect for the solution of the initial value problem of ordinary differential equations. The essential result is a divergence theorem in dependence of the polynomial degree and the defect of the spline functions. In this second part the convergent procedures are investigated and two convergence theorems are proved. Furthermore the question is treated, whether the convergent procedures are appropriate for the numerical solution of stiff equations. The paper is finished by a convergence theorem for a procedure producing spline approximations in a natural way by the discrete approxima…
Guaranteed Error Bounds for Conforming Approximations of a Maxwell Type Problem
2009
This paper is concerned with computable error estimates for approximations to a boundary-value problem $$\mathrm{curl}\ {\mu }^{-1}\mathrm{curl}\ u + {\kappa }^{2}u = j\quad \textrm{ in }\Omega ,$$ where μ > 0 and κ are bounded functions. We derive a posteriori error estimates valid for any conforming approximations of the considered problems. For this purpose, we apply a new approach that is based on certain transformations of the basic integral identity. The consistency of the derived a posteriori error estimates is proved and the corresponding computational strategies are discussed.
Extensions and intentions in the rough set theory
1998
Abstract The approach to rough set theory proposed in this paper is based on the mutual correspondence of the concepts of extension and intension. It is different from the well-known approaches in the literature in that the upper approximations and the lower approximations of ‘unknown’ sets are considered as certain families of ‘known’ sets. This approach makes it possible to formulate necessary and sufficient conditions for the existence of operations on rough sets, which are analogous to classical operations on sets. The basic results presented in this paper, based on certain ideas of the second author, were formulated by the first author in his doctoral dissertation prepared under the su…
On the Structure of Bispecial Sturmian Words
2013
A balanced word is one in which any two factors of the same length contain the same number of each letter of the alphabet up to one. Finite binary balanced words are called Sturmian words. A Sturmian word is bispecial if it can be extended to the left and to the right with both letters remaining a Sturmian word. There is a deep relation between bispecial Sturmian words and Christoffel words, that are the digital approximations of Euclidean segments in the plane. In 1997, J. Berstel and A. de Luca proved that \emph{palindromic} bispecial Sturmian words are precisely the maximal internal factors of \emph{primitive} Christoffel words. We extend this result by showing that bispecial Sturmian wo…
Remarks on quadratic Hamiltonians in spaceflight mechanics
2006
A particular family of Hamiltonian functions is considered. Such functions are quadratic in the moment variables and arise in spaceflight mechanics when the averaged system of energy minimizing trajectories of the Kepler equation is computed. An important issue of perturbation theory and averaging is to provide integrable approximations of nonlinear systems. It turns out that such integrability properties hold here.