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排序方式: 共有91条查询结果,搜索用时 15 毫秒
1.
This article proposes a global, chaos-based procedure for the discretization of functionals of Brownian motion into functionals of a Poisson process with intensity . Under this discretization we study the weak convergence, as the intensity of the underlying Poisson process goes to infinity, of Poisson functionals and their corresponding Malliavin-type derivatives to their Wiener counterparts. In addition, we derive a convergence rate of for the Poisson discretization of Wiener functionals by combining the multivariate Chen–Stein method with the Malliavin calculus. Our proposed sufficient condition for establishing the mentioned convergence rate involves the kernel functions in the Wiener chaos, yet we provide examples, especially the discretization of some common path dependent Wiener functionals, to which our results apply without committing the explicit computations of such kernels. To the best our knowledge, these are the first results in the literature on the universal convergence rate of a global discretization of general Wiener functionals. 相似文献
2.
X. Z. Wang F. V. Buontempo A. Young D. Osborn 《SAR and QSAR in environmental research》2013,24(5):451-471
Recent literature has demonstrated the applicability of genetic programming to induction of decision trees for modelling toxicity endpoints. Compared with other decision tree induction techniques that are based upon recursive partitioning employing greedy searches to choose the best splitting attribute and value at each node that will necessarily miss regions of the search space, the genetic programming based approach can overcome the problem. However, the method still requires the discretization of the often continuous-valued toxicity endpoints prior to the tree induction. A novel extension of this method, YAdapt, is introduced in this work which models the original continuous endpoint by adaptively finding suitable ranges to describe the endpoints during the tree induction process, removing the need for discretization prior to tree induction and allowing the ordinal nature of the endpoint to be taken into account in the models built. 相似文献
3.
For a system of smooth Jordan curves and arcs asymptotics for Christoffel functions is established. A separate new method is developed to handle the upper and lower estimates. In the course to the upper bound a theorem of Widom on the norm of Chebyshev polynomials is generalized. 相似文献
4.
Matti Koivu 《Mathematical Programming》2005,103(3):463-485
This paper studies the use of randomized Quasi-Monte Carlo methods (RQMC) in sample approximations of stochastic programs. In numerical integration, RQMC methods often substantially reduce the variance of sample approximations compared to Monte Carlo (MC). It seems thus natural to use RQMC methods in sample approximations of stochastic programs. It is shown, that RQMC methods produce epi-convergent approximations of the original problem. RQMC and MC methods are compared numerically in five different portfolio management models. In the tests, RQMC methods outperform MC sampling substantially reducing the sample variance and bias of optimal values in all the considered problems. 相似文献
5.
The paper refers to the solution of the integral equation for the acceleration (or pressure) potential for the study of subsonic linearized unsteady flow in view of aeroelastic applications. The case considered is relevant to a trapezoidal wing infinitely thin surface without discontinuities. As is well known [1, 2], the kernel of the integral equation exhibits three singularities, two of which are integrable in elementary form, whereas, for the third one integration in principal part according to Hadamard's rule is necessary. The kernel is therefore reworked in such a way that all the singularities are separated from the regular part, and eventually the discretization is performed in such a way that only the regular part is to be recalculated for each new value of the reduced frequency. Convergence tests, comparison with other methods of solution, and time saving associated with the technique of separation are also shown.Sommario. II lavoro tratta la risoluzione del problema relativo alla equazione integrale nel potenziale di accelerazione (o di pressione) per lo studio di una corrente subsonica linearizzata nonstazionaria, in vista di applicazioni aeroelastiche. Il caso considerato è quello di una superficie alare a pianta trapezoidale in assenza di discontinuità di spessore infinitesimo. Come è noto [1, 2], il nucleo della equazione integrale in parola presenta tre singolarità, due sole delle quali sono integrabili in forma elementare, (o riconducibili ad essa), mentre per la terza è necessario far ricorso alla integrazione in parte principale alla Hadamard. Il nucleo stesso viene quindi rielaborato in modo da isolare tutte le singolarità dalla componente regolare del nucleo; si procede così alla discretizzazione dell' equazione integrale, e, per ogni valore della frequenza ridotta, va ricalcolata solo la parte regolare della matrice risolvente. Vengono poi effettuati tests di convergenza, confronti con altri metodi di soluzione, analisi sui tempi di calcolo e risparmio di tempo di calcolo dovuto alla tecnica di separazione. 相似文献
6.
On the Discretization of Distributed-Parameter Systems with Quadratic and Cubic Nonlinearities 总被引:2,自引:0,他引:2
Approximate methods for analyzing the vibrations of an Euler--Bernoulli beam resting on a nonlinear elastic foundation are discussed. The cases of primary resonance (
n
) and subharmonic resonance of order one-half ( 2
n
), where is the excitation frequency and
n
is the natural frequency of the nth mode of the beam, are investigated. Approximate solutions based on discretization via the Galerkin method are contrasted with direct application of the method of multiple scales to the governing partial-differential equation and boundary conditions. The amplitude and phase modulation equations show that single-mode discretization leads to erroneous qualitative as well as quantitative predictions. Regions of softening (hardening) behavior of the system, the spatial dependence of the response drift, and frequency-response curves are numerically evaluated and compared using both approaches. 相似文献
7.
Wenrui Hao Jonathan D. Hauenstein Bei Hu Andrew J. Sommese 《Applied mathematics and computation》2011,218(6):2661-2669
The growth of tumors can be modeled as a free boundary problem involving partial differential equations. We consider one such model and compute steady-state solutions for this model. These solutions include radially symmetric solutions where the free boundary is a sphere and nonradially symmetric solutions. Linear and nonlinear stability for these solutions are determined numerically. 相似文献
8.
A discretization algorithm is proposed by Haar wavelet approximation theory for the fractional order integral. In this paper, the integration time is divided into two parts, one presents the effect of the past sampled data, calculated by the iterative method, and the other presents the effect of the recent sampled data at a fixed time interval, calculated by the Haar wavelet. This method can reduce the amount of the stored data effectively and be applied to the design of discrete-time fractional order PID controllers. Finally, several numerical examples and simulation results are given to illustrate the validity of this discretization algorithm. 相似文献
9.
In this paper, a two-scale higher-order finite element discretization scheme is proposed and analyzed for a Schroedinger equation on tensor product domains. With the scheme, the solution of the eigenvalue problem on a fine grid can be reduced to an eigenvalue problem on a much coarser grid together with some eigenvalue problems on partially fine grids. It is shown theoretically and numerically that the proposed two-scale higher-order scheme not only significantly reduces the number of degrees of freedom but also produces very accurate approximations. 相似文献
10.
Adaptive strategies are a necessary tool to make finite element analysis applicable to engineering practice. In this paper, attention is restricted to mesh adaptivity. Traditionally, the most common mesh adaptive strategies for linear problems are used to reach a prescribed accuracy. This goal is best met with an h-adaptive scheme in combination with an error estimator. In an industrial context, the aim of the mechanical simulations in engineering design is not only to obtain greatest quality but more often a compromise between the desired quality and the computation cost (CPU time, storage, software, competence, human cost, computer used). In this paper, we propose the use of alternative mesh refinement criteria with an h-adaptive procedure for 3D elastic problems. The alternative mesh refinement criteria (MR) are based on: prescribed number of elements with maximum accuracy, prescribed CPU time with maximum accuracy and prescribed memory size with maximum accuracy. These adaptive strategies are based on a technique of error in constitutive relation (the process could be used with other error estimators) and an efficient adaptive technique which automatically takes into account the steep gradient areas. This work proposes a 3D method of adaptivity with the latest version of the INRIA automatic mesh generator GAMHIC3D. 相似文献