Approximation Methods (approximation + methods)

Distribution by Scientific Domains


Selected Abstracts


Approximation methods for reliability-based design optimization problems

GAMM - MITTEILUNGEN, Issue 2 2007
Irfan Kaymaz
Abstract Deterministic optimum designs are obtained without considering of uncertainties related to the problem parameters such as material parameters (yield stress, allowable stresses, moment capacities, etc.), external loadings, manufacturing errors, tolerances, cost functions, which could lead to unreliable designs, therefore several methods have been developed to treat uncertainties in engineering analysis and, more recently, to carry out design optimization with the additional requirement of reliability, which referred to as reliability-based design optimization. In this paper, two most common approaches for reliability-based design optimization are reviewed, one of which is reliability-index based approach and the other performancemeasure approach. Although both approaches can be used to evaluate the probabilistic constraint, their use can be prohibitive when the associated function evaluation required by the probabilistic constraint is expensive, especially for real engineering problems. Therefore, an adaptive response surface method is proposed by which the probabilistic constraint is replaced with a simple polynomial function, thus the computational time can be reduced significantly as presented in the example given in this paper. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]


High order interpolation methods for semi-Lagrangian models of mobile-bed hydrodynamics on Cartesian grids with cut cells

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10-11 2005
Giorgio Rosatti
Abstract High order approximation methods based on radial basis functions are applied to the extension of semi-Lagrangian shallow water models to staggered Cartesian meshes with cut boundary cells. The accuracy and efficiency of the resulting semi-Lagrangian method is demonstrated by test cases simulating open channel flow. The derivative reconstruction provided by radial basis function interpolators is also employed successfully in the discretization of sediment transport models for mobile bed river flow. Copyright © 2005 John Wiley & Sons, Ltd. [source]


Constrained robust sampled-data control for nonlinear uncertain systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2002
Li-Sheng Hu
Abstract In industrial process control, computer control, which makes the closed-loop system a sampled-data one containing both continuous- and discrete-time signals, is widely used. In contrast with traditional approximation methods, sampled-data synthesis, a direct digital controller design procedure without approximation, has received increasing attention during the past few years. However, many of the existing results cannot be applied to sampled-data control design for the uncertain systems. In this paper, a result of robust asymptotic stability of sampled-data systems with constraints on the state is presented based on a result on practical stability for these systems. Then the robust sampled-data control for a class of uncertain nonlinear systems with constraints on the output is developed. The problem is formulated from vehicle steering control with constraint on the side slip angle of body. The result is described by some matrix inequalities which could be solved by an iterative algorithm based on the linear matrix inequality technique. Finally, a numerical example is presented to demonstrate the result. Copyright © 2002 John Wiley & Sons, Ltd. [source]


STOCK LIQUIDATION VIA STOCHASTIC APPROXIMATION USING NASDAQ DAILY AND INTRA-DAY DATA

MATHEMATICAL FINANCE, Issue 1 2006
G. Yin
By focusing on computational aspects, this work is concerned with numerical methods for stock selling decision using stochastic approximation methods. Concentrating on the class of decisions depending on threshold values, an optimal stopping problem is converted to a parametric stochastic optimization problem. The algorithms are model free and are easily implementable on-line. Convergence of the algorithms is established, second moment bound of estimation error is obtained, and escape probability from a neighborhood of the true parameter is also derived. Numerical examples using both daily closing prices and intra-day data are provided to demonstrate the performance of the algorithms. [source]


Interaction of elementary waves for scalar conservation laws on a bounded domain

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2003
Hongxia Liu
Abstract This paper is concerned with the interaction of elementary waves on a bounded domain for scalar conservation laws. The structure and large time asymptotic behaviours of weak entropy solution in the sense of Bardos et al. (Comm. Partial Differential Equations 1979; 4: 1017) are clarified to the initial,boundary problem for scalar conservation laws ut+,(u)x=0 on (0,1) × (0,,), with the initial data u(x,0)=u0(x):=um and the boundary data u(0,t)=u -,u(1,t)=u+, where u±,um are constants, which are not equivalent, and ,,C2 satisfies ,,,>0, ,(0)=f,(0)=0. We also give some global estimates on derivatives of the weak entropy solution. These estimates play important roles in studying the rate of convergence for various approximation methods to scalar conservation laws. Copyright © 2003 John Wiley & Sons, Ltd. [source]


Ishikawa iterative process with errors for nonlinear equations of generalized monotone type in Banach spaces

MATHEMATISCHE NACHRICHTEN, Issue 10 2005
Ljubomir B.
Abstract The concept of the operators of generalized monotone type is introduced and iterative approximation methods for a fixed point of such operators by the Ishikawa and Mann iteration schemes {xn} and {yn} with errors is studied. Let X be a real Banach space and T : D , X , 2D be a multi-valued operator of generalized monotone type with fixed points. A new general lemma on the convergence of real sequences is proved and used to show that {xn} converges strongly to a unique fixed point of T in D. This result is applied to the iterative approximation method for solutions of nonlinear equations with generalized strongly accretive operators. Our results generalize many of know results. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]


Bayesian strategies for dynamic pricing in e-commerce

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 3 2007
Eric Cope
Abstract E-commerce platforms afford retailers unprecedented visibility into customer purchase behavior and provide an environment in which prices can be updated quickly and cheaply in response to changing market conditions. This study investigates dynamic pricing strategies for maximizing revenue in an Internet retail channel by actively learning customers' demand response to price. A general methodology is proposed for dynamically pricing information goods, as well as other nonperishable products for which inventory levels are not an essential consideration in pricing. A Bayesian model of demand uncertainty involving the Dirichlet distribution or a mixture of such distributions as a prior captures a wide range of beliefs about customer demand. We provide both analytic formulas and efficient approximation methods for updating these prior distributions after sales data have been observed. We then investigate several strategies for sequential pricing based on index functions that consider both the potential revenue and the information value of selecting prices. These strategies require a manageable amount of computation, are robust to many types of prior misspecification, and yield high revenues compared to static pricing and passive learning approaches. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007 [source]


A Fourier optics approach to the dynamical theory of X-ray diffraction , continuously deformed crystals

ACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2004
Giovanni Mana
X-ray diffraction in continuously deformed crystals is considered by application of Fourier optics and from the viewpoint of the analogy between X-ray dynamics and the motion of two-level systems in quantum mechanics. Different forms of Takagi's equations are traced back to a common framework and it is shown that they are different ways to represent the same propagation equation. A novel way to solve Takagi's equations in the presence of a constant strain gradient is presented and approximation methods derived from quantum mechanics are considered. Crystal deformation in X-ray interferometry and two-crystal spectrometry are discussed and it is demonstrated that Si lattice-parameter measurements depend on the diffracting plane spacing on the crystal surface. [source]