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Henk J.A.M. Heijmans Batrice Pesquet-Popescu Gemma Piella 《Applied and Computational Harmonic Analysis》2005,18(3):252-281
In this paper, we propose a technique for building adaptive wavelets by means of an extension of the lifting scheme. Our scheme comprises an adaptive update lifting step and a fixed prediction lifting step. The adaptivity consists hereof that the system can choose between two different update filters, and that this choice is triggered by the local gradient of the original signal. If the gradient is large (in some seminorm sense) it chooses one filter, if it is small the other. We derive necessary and sufficient conditions for the invertibility of such an adaptive system for various scenarios. Furthermore, we present some examples to illustrate our theoretical results. 相似文献
4.
Solving Multi-dimensional Evolution Problems with Localized Structures using Second Generation Wavelets 总被引:2,自引:0,他引:2
Oleg V. Vasilyev 《International Journal of Computational Fluid Dynamics》2013,27(2):151-168
A dynamically adaptive numerical method for solving multi-dimensional evolution problems with localized structures is developed. The method is based on the general class of multi-dimensional second-generation wavelets and is an extension of the second-generation wavelet collocation method of Vasilyev and Bowman to two and higher dimensions and irregular sampling intervals. Wavelet decomposition is used for grid adaptation and interpolation, while O ( N ) hierarchical finite difference scheme, which takes advantage of wavelet multilevel decomposition, is used for derivative calculations. The prowess and computational efficiency of the method are demonstrated for the solution of a number of two-dimensional test problems. 相似文献
5.
Hande Yaman 《Mathematical Programming》2006,106(2):365-390
We consider the vehicle routing problem where one can choose among vehicles with different costs and capacities to serve the
trips. We develop six different formulations: the first four based on Miller-Tucker-Zemlin constraints and the last two based
on flows. We compare the linear programming bounds of these formulations. We derive valid inequalities and lift some of the
constraints to improve the lower bounds. We generalize and strengthen subtour elimination and generalized large multistar
inequalities. 相似文献
6.
Kazuma Shimomoto 《代数通讯》2017,45(3):1057-1075
In this article, we discuss the semicontinuity problem of certain properties on fibers for a morphism of schemes. One aspect of this problem is local. Namely, we consider properties of schemes at the level of local rings, in which the main results are established by solving the lifting and localization problems for local rings. In particular, we obtain the localization theorems in the case of seminormal and F-rational rings, respectively. Another aspect of this problem is global, which is often related to the vanishing problem of certain higher direct image sheaves. As a test example, we consider the deformation of the global F-regularity. 相似文献
7.
Solving diffusion equation using wavelet method 总被引:1,自引:0,他引:1
Xuefeng ChenJiawei Xiang 《Applied mathematics and computation》2011,217(13):6426-6432
A wavelet-based numerical method based on wavelets of Hermite cubic splines is presented for computing singularly perturbed convection-dominated diffusion equation. The advantages of the method are explained. To improve the accuracy of singular areas, wavelets are configured hierarchically for solving algebraic equations. Numerical examples show that the proposed method has good efficiency and precision. 相似文献
8.
In this survey we attempt to give a unified presentation of a variety of results on the lifting of valid inequalities, as
well as a standard procedure combining mixed integer rounding with lifting for the development of strong valid inequalities
for knapsack and single node flow sets. Our hope is that the latter can be used in practice to generate cutting planes for
mixed integer programs.
The survey contains essentially two parts. In the first we present lifting in a very general way, emphasizing superadditive
lifting which allows one to lift simultaneously different sets of variables. In the second, our procedure for generating strong
valid inequalities consists of reduction to a knapsack set with a single continuous variable, construction of a mixed integer
rounding inequality, and superadditive lifting. It is applied to several generalizations of the 0–1 single node flow set.
This paper appeared in 4OR, 1, 173–208 (2003).
The first author is supported by the FNRS as a chercheur qualifié. This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction
initiated by the Belgian State, Prime Minister’s Office, Science Policy Programming. The scientific responsibility is assumed
by the authors. 相似文献
9.
本文首先给出了一个右连续上鞅的SD提升,在引进S-上鞅和强S-上鞅概念之后,研究了一一致可积上鞅与S-上鞅,类上鞅与强S-上鞅之间的关系,并得到了S-上鞅与强S-上鞅的许多性质,作为其直接结果,给出了类上鞅的Doob-MNeyer分解。 相似文献
10.
Rajendra K. Bera 《国际流体数值方法杂志》1989,9(3):251-262
Theodorsen's method for calculating the incompressible potential flow past an aerofoil is viewed afresh. It is found that some simple modifications to the computational process make the computations relatively faster, easier and more accurate. The new modifications are applicable to the analysis of conventional aerofoils with up to moderate thickness and camber ratios. Several examples are presented to show the effectiveness of the modifications. 相似文献