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Approximation Properties (approximation + property)

Distribution by Scientific Domains

Engineering	80%

Selected Abstracts

APPROXIMATION PROPERTIES OF TP MODEL FORMS AND ITS CONSEQUENCES TO TPDC DESIGN FRAMEWORK

ASIAN JOURNAL OF CONTROL, Issue 3 2007
Domonkos Tikk
ABSTRACT Tensor Product Distributed Compensation (TPDC) is a recently established controller design framework, that links TP model transformation and Parallel Distributed Compensation (PDC) framework. TP model transformation converts different models to a common representational form: the TP model form. The primary aim of this paper is to investigate the approximation capabilities of TP model forms, because the universal applicability of TPDC framework strongly relies on it. We point out that the set of functions that can be approximated arbitrarily well by TP forms with bounded number of components lies no-where dense in the set of continuous functions. Consequently, in a class of control problems this property necessitates the usage of tradeoff techniques between the accuracy and the complexity of the TP form, which is easily feasible within the TPDC framework unlike in analytic models. [source]

On the quadrilateral Q2,P1 element for the Stokes problem

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2002
Daniele Boffi
Abstract The Q2 , P1 approximation is one of the most popular Stokes elements. Two possible choices are given for the definition of the pressure space: one can either use a global pressure approximation (that is on each quadrilateral the finite element space is spanned by 1 and by the global co-ordinates x and y) or a local approach (consisting in generating the local space by means of the constants and the local curvilinear co-ordinates on each quadrilateral , and ,). The former choice is known to provide optimal error estimates on general meshes. This has been shown, as it is standard, by proving a discrete inf,sup condition. In the present paper we check that the latter approach satisfies the inf,sup condition as well. However, recent results on quadrilateral finite elements bring to light a lack in the approximation properties for the space coming out from the local pressure approach. Numerical results actually show that the second choice (local or mapped pressure approximation) is suboptimally convergent. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Approximation representations for reals and their wtt-degrees

MLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 4-5 2004
George Barmpalias
Abstract We study the approximation properties of computably enumerable reals. We deal with a natural notion of approximation representation and study their wtt-degrees. Also, we show that a single representation may correspond to a quite diverse variety of reals. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Approximation and complexity trade-off by TP model transformation in controller design: A case study of the TORA system,

ASIAN JOURNAL OF CONTROL, Issue 5 2010
Zoltán Petres
Abstract The main objective of the paper is to study the approximation and complexity trade-off capabilities of the recently proposed tensor product distributed compensation (TPDC) based control design framework. The TPDC is the combination of the TP model transformation and the parallel distributed compensation (PDC) framework. The Tensor Product (TP) model transformation includes an Higher Order Singular Value Decomposition (HOSVD)-based technique to solve the approximation and complexity trade-off. In this paper we generate TP models with different complexity and approximation properties, and then we derive controllers for them. We analyze how the trade-off effects the model behavior and control performance. All these properties are studied via the state feedback controller design of the Translational Oscillations with an Eccentric Rotational Proof Mass Actuator (TORA) System. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

A finite-volume particle method for conservation laws on moving domains

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2008
D. Teleaga
Abstract The paper deals with the finite-volume particle method (FVPM), a relatively new method for solving hyperbolic systems of conservation laws. A general formulation of the method for bounded and moving domains is presented. Furthermore, an approximation property of the reconstruction formula is proved. Then, based on a two-dimensional test problem posed on a moving domain, a special Ansatz for the movement of the particles is proposed. The obtained numerical results indicate that this method is well suited for such problems, and thus a first step to apply the FVPM to real industrial problems involving free boundaries or fluid,structure interaction is taken. Finally, we perform a numerical convergence study for a shock tube problem and a simple linear advection equation. Copyright © 2008 John Wiley & Sons, Ltd. [source]