Search results for "approximations"
showing 10 items of 28 documents
Controlled polyhedral sweeping processes: existence, stability, and optimality conditions
2021
This paper is mainly devoted to the study of controlled sweeping processes with polyhedral moving sets in Hilbert spaces. Based on a detailed analysis of truncated Hausdorff distances between moving polyhedra, we derive new existence and uniqueness theorems for sweeping trajectories corresponding to various classes of control functions acting in moving sets. Then we establish quantitative stability results, which provide efficient estimates on the sweeping trajectory dependence on controls and initial values. Our final topic, accomplished in finite-dimensional state spaces, is deriving new necessary optimality and suboptimality conditions for sweeping control systems with endpoint constrain…
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.
Approximating hidden chaotic attractors via parameter switching.
2018
In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration. In Refs. 1–3, it is proved that the attractors of a chaotic system, considered as the unique numerical …
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…
Partial self-consistency and analyticity in many-body perturbation theory: Particle number conservation and a generalized sum rule
2016
We consider a general class of approximations which guarantees the conservation of particle number in many-body perturbation theory. To do this we extend the concept of $\Phi$-derivability for the self-energy $\Sigma$ to a larger class of diagrammatic terms in which only some of the Green's function lines contain the fully dressed Green's function $G$. We call the corresponding approximations for $\Sigma$ partially $\Phi$-derivable. A special subclass of such approximations, which are gauge-invariant, is obtained by dressing loops in the diagrammatic expansion of $\Phi$ consistently with $G$. These approximations are number conserving but do not have to fulfill other conservation laws, such…
Analysis and approximation of one-dimensional scalar conservation laws with general point constraints on the flux
2016
We introduce and analyze a class of models with nonlocal point constraints for traffic flow through bottlenecks, such as exits in the context of pedestrians traffic and reduction of lanes on a road under construction in vehicular traffic. Constraints are defined based on data collected from non-local in space and/or in time observations of the flow. We propose a theoretical analysis and discretization framework that permits to include different data acquisition strategies; a numerical comparison is provided. Nonlocal constraint allows to model, e.g., the irrational behavior (" panic ") near the exit observed in dense crowds and the capacity drop at tollbooth in vehicular traffic. Existence …