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1.
<正>This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes,one is analogous to Douglas finite difference scheme with second-order splitting error,the other two schemes have third-order splitting error,and the last one is an extended LOD scheme.The L~2 norm and H~1 semi-norm error estimates are obtained for the first scheme and second one,respectively.Finally,two numerical examples are provided to illustrate the efficiency and accuracy of the methods.  相似文献   

2.
<正>In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging,scientific computing,reverse engineering and geometric modelling.The reconstructed surface is obtained by continuously deforming an initial surface following the Partial Differential Equation(PDE)-based diffusion model derived by a minimal volume-like variational formulation.The evolution is driven both by the distance from the data set and by the curvature analytically computed by it.The distance function is computed by implicit local interpolants defined in terms of radial basis functions.Space discretization of the PDE model is obtained by finite co-volume schemes and semi-implicit approach is used in time/scale.The use of a level set method for the numerical computation of the surface reconstruction allows us to handle complex geometry and even changing topology, without the need of user-interaction.Numerical examples demonstrate the ability of the proposed method to produce high quality reconstructions.Moreover,we show the effectiveness of the new approach to solve hole filling problems and Boolean operations between different data sets.  相似文献   

3.
Generalizing wavelets by adding desired redundancy and flexibility,framelets(i.e.,wavelet frames)are of interest and importance in many applications such as image processing and numerical algorithms.Several key properties of framelets are high vanishing moments for sparse multiscale representation,fast framelet transforms for numerical efficiency,and redundancy for robustness.However,it is a challenging problem to study and construct multivariate nonseparable framelets,mainly due to their intrinsic connections to factorization and syzygy modules of multivariate polynomial matrices.Moreover,all the known multivariate tight framelets derived from spline refinable scalar functions have only one vanishing moment,and framelets derived from refinable vector functions are barely studied yet in the literature.In this paper,we circumvent the above difficulties through the approach of quasi-tight framelets,which behave almost identically to tight framelets.Employing the popular oblique extension principle(OEP),from an arbitrary compactly supported M-refinable vector functionφwith multiplicity greater than one,we prove that we can always derive fromφa compactly supported multivariate quasi-tight framelet such that:(i)all the framelet generators have the highest possible order of vanishing moments;(ii)its associated fast framelet transform has the highest balancing order and is compact.For a refinable scalar functionφ(i.e.,its multiplicity is one),the above item(ii)often cannot be achieved intrinsically but we show that we can always construct a compactly supported OEP-based multivariate quasi-tight framelet derived fromφsatisfying item(i).We point out that constructing OEP-based quasi-tight framelets is closely related to the generalized spectral factorization of Hermitian trigonometric polynomial matrices.Our proof is critically built on a newly developed result on the normal form of a matrix-valued filter,which is of interest and importance in itself for greatly facilitating the study of refinable vector functions and multiwavelets/multiframelets.This paper provides a comprehensive investigation on OEP-based multivariate quasi-tight multiframelets and their associated framelet transforms with high balancing orders.This deepens our theoretical understanding of multivariate quasi-tight multiframelets and their associated fast multiframelet transforms.  相似文献   

4.
<正>Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term.A regularized convex term can usually preserve the image edges well in the restored image.In this paper,we consider a class of convex and edge-preserving regularization functions,i.e.,multiplicative half-quadratic regularizations,and we use the Newton method to solve the correspondingly reduced systems of nonlinear equations.At each Newton iterate,the preconditioned conjugate gradient method,incorporated with a constraint preconditioner,is employed to solve the structured Newton equation that has a symmetric positive definite coefficient matrix. The eigenvalue bounds of the preconditioned matrix are deliberately derived,which can be used to estimate the convergence speed of the preconditioned conjugate gradient method.We use experimental results to demonstrate that this new approach is efficient, and the effect of image restoration is reasonably well.  相似文献   

5.
We introduce a class of singular integral operators on product domains along twisted surfaces.We prove that the operators are bounded on Lp provided that the kernels satisfy weak conditions.  相似文献   

6.
<正>The gas-kinetic theory based flux splitting method has been successfully proposed for solving one-and two-dimensional ideal magnetohydrodynamics by Xu et al. [J.Comput.Phys.,1999;2000],respectively.This paper extends the kinetic method to solve three-dimensional ideal magnetohydrodynamics equations,where an adaptive parameter 17 is used to control the numerical dissipation in the flux splitting method. Several numerical examples are given to demonstrate that the proposed method can achieve high numerical accuracy and resolve strong discontinuous waves in three dimensional ideal MHD problems.  相似文献   

7.
本文主要讨论组合地图列举问题.刘的一部专著中提出了一个判定两个地图是否同构的算法.该算法的时间复杂度为O(m2),其中m为下图的规模.在此基础上,本文给出一个用于地图列举以及进而计算任意连通下图的地图亏格分布的通用算法.本文所得结果比之前文献中所给结果更优.  相似文献   

8.
<正>The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented.Existence and uniqueness of optimal solutions is proved. A collective Gauss-Seidel scheme and a multigrid scheme are discussed.Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.  相似文献   

9.
This paper is concerned with a singular second-order nonlinear boundary value problem with a time depending on derivative operator and posed on the positive half-line. The nonlinearity is derivative-dependent, which has singularities at t=0 and/or x=0, and may change sign. The method of the upper and lower solutions on unbounded domains combined with the topological degree theory are employed to prove the existence and multiplicity of solutions.  相似文献   

10.
In this paper,we use a unified framework to study Poisson stable(including stationary,periodic,quasi-periodic,almost periodic,almost automorphic,Birkhoff recurrent,almost recurrent in the sense of Bebutov,Levitan almost periodic,pseudo-periodic,pseudo-recurrent and Poisson stable)solutions for semilinear stochastic differential equations driven by infinite dimensional L′evy noise with large jumps.Under suitable conditions on drift,diffusion and jump coefficients,we prove that there exist solutions which inherit the Poisson stability of coefficients.Further we show that these solutions are globally asymptotically stable in square-mean sense.Finally,we illustrate our theoretical results by several examples.  相似文献   

11.
ONTHEBOUNDEDNESSCONDITIONSFORSOLUTIONSOFAAUTONOMOUSDIFFERENTIALSYSTEM¥HuangLihong(黄立宏);WangZhicheng(王志成)(HunanUniversity,湖南大学...  相似文献   

12.
研究了一类广义 Liénard系统dxdt=p(y) -F(x) ,  dydt=-g(x) (E)解的有界性 .首先获得了系统 (E)存在无界解的两个新的充分条件 ,然后获得系统 (E)所有解正向有界的若干充分条件和充要条件 ,所获结果改进和扩展了文 [1 -2 ]中的相应结果 .  相似文献   

13.
非线性泛函微分方程解的性态   总被引:13,自引:0,他引:13  
本文给出了一类非线性泛函微分方程解的性态的若干充要条件,推广了[1]的某些结论.  相似文献   

14.
In mathematical programming, constraint qualifications are essential elements for duality theory. Recently, necessary and sufficient constraint qualifications for Lagrange duality results have been investigated. Also, surrogate duality enables one to replace the problem by a simpler one in which the constraint function is a scalar one. However, as far as we know, a necessary and sufficient constraint qualification for surrogate duality has not been proposed yet. In this paper, we propose necessary and sufficient constraint qualifications for surrogate duality and surrogate min–max duality, which are closely related with ones for Lagrange duality.  相似文献   

15.
Korenevskii  D. G. 《Mathematical Notes》2001,70(1-2):192-205
We give spectral and algebraic coefficient criteria (necessary and sufficient conditions) as well as sufficient algebraic coefficient conditions for the Lyapunov asymptotic stability of solutions to systems of linear deterministic or stochastic delay difference equations with continuous time under white noise coefficient perturbations for the case in which all delay ratios are rational. For stochastic systems, mean-square asymptotic stability is studied. The Lyapunov function method is used. Our criteria on algebraic coefficients and our sufficient conditions are stated in terms of matrix Lyapunov equations (for deterministic systems) and matrix Sylvester equations (for stochastic systems).  相似文献   

16.
A well known bidirectional associative memory (BAM) model is generalized with the introduction of discrete time delays in the leakage (or forgetting) terms. By using a model transformation, the system is converted to one of a neutral delay system. Two sets of delay dependent sufficient conditions are derived for the existence of a unique equilibrium as well as its asymptotic and exponential stability. The methods of degenerate Lyapunov-Kravsovskii functionals and inequalities together with some properties of M-matrices are used in the derivation of sufficient conditions. In the absence of leakage delays, the sufficient conditions lead to some known sufficient conditions.  相似文献   

17.
The concepts of domination structures and non-dominated decisions are extended to dynamic decision problems. Previously derived results are utilized in conjunction with optimal control theory to deduce necessary as well as sufficient conditions for nondominated controls. Cone convexity for dynamic problems is discussed, and sufficient conditions are given for a class of linear systems.  相似文献   

18.
两类模糊系统作为通用逼近器的充分条件的比较与分析   总被引:2,自引:0,他引:2  
对现有的Mamdani模糊系统和T-S模糊系统作为通用逼近器的充分条件作比较分析,提出了通过三种不同算法获得的单输入单输出Mamdani模糊系统作为通用逼近器的充分条件的保守性比较定理。  相似文献   

19.
For polynomial splines as well as for Chebyshev splines, it is known that total positivity of the connection matrices is sufficient to obtain B-spline bases. In this paper we give a necessary and sufficient condition for the existence of B-bases (or, equivalently, of blossoms) for splines with connection matrices and with sections in different four-dimensional extended Chebyshev spaces.  相似文献   

20.
In this paper we investigate some existence questions of positive semi-definite solutions for certain classes of matrix equations known as the generalized Lyapunov equations. We present sufficient and necessary conditions for certain equations and only sufficient for others.  相似文献   

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