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1.
This paper is concerned with the ill-posed problems of identifying a parameter in an elliptic equation which appears in many applications in science and industry. Its solution is obtained by applying trust region method to a nonlinear least squares error problem.Trust region method has long been a popular method for well-posed problems. This paper indicates that it is also suitable for ill-posed problems, Numerical experiment is given to compare the trust region method with the Tikhonov regularization method. It seems that the trust region method is more promising.  相似文献   

2.
Random weighting method for Cox’s proportional hazards model   总被引:1,自引:0,他引:1  
Variance of parameter estimate in Cox’s proportional hazards model is based on asymptotic variance. When sample size is small, variance can be estimated by bootstrap method. However, if censoring rate in a survival data set is high, bootstrap method may fail to work properly. This is because bootstrap samples may be even more heavily censored due to repeated sampling of the censored observations. This paper proposes a random weighting method for variance estimation and confidence interval estimation for proportional hazards model. This method, unlike the bootstrap method, does not lead to more severe censoring than the original sample does. Its large sample properties are studied and the consistency and asymptotic normality are proved under mild conditions. Simulation studies show that the random weighting method is not as sensitive to heavy censoring as bootstrap method is and can produce good variance estimates or confidence intervals.  相似文献   

3.
This paper describes the spectral method for numerically solving Zakharov equation with periodicboundary conditions. This method is spectral method for spatial variable and difference method fortime variable. We make error estimation of approximate solution and prove the convergence of spectralmethod. We had given the convergence rate. Also, we prove the stability of approximate method forinitial values.  相似文献   

4.
A NEW TRUST REGION DOGLEG METHOD FOR UNCONSTRAINED OPTIMIZATION   总被引:1,自引:0,他引:1  
Abstract. This paper presents a new trust region dogleg method for unconstrained optimization.The method can deal with the case when the Hessian B of quadratic models is indefinite. It isproved that the method is globally convergent and has a quadratic convergence rate if Under certain conditions, the solution obtained by the method is even a second order  相似文献   

5.
In this paper, we give a hybrid method to numerically solve the inverse open cavity scattering problem for cavity shape, given the scattered solution on the opening of the cavity. This method is a hybrid between an iterative method and an integral equations method for solving the Cauchy problem. The idea of this hybrid method is simple, the operation is easy, and the computation cost is small. Numerical experiments show the feasibility of this method, even for cases with noise.  相似文献   

6.
For an integrator when applied to a highly oscillatory system,the near conservation of the oscillatory energy over long times is an important aspect.In this paper,we study the long-time near conservation of oscillatory energy for the adapted average vector field(AAVF)method when applied to highly oscillatory Hamiltonian systems.This AAVF method is an extension of the average vector field method and preserves the total energy of highly oscillatory Hamiltonian systems exactly.This paper is devoted to analysing another important property of AAVF method,i.e.,the near conservation of its oscillatory energy in a long term.The long-time oscillatory energy conservation is obtained via constructing a modulated Fourier expansion of the AAVF method and deriving an almost invariant of the expansion.A similar result of the method in the multi-frequency case is also presented in this paper.  相似文献   

7.
A NEW NUMERICAL METHOD FOR TWO-PHASE IMMISCIBLE INCOMPRESSIBLE PROBLEM   总被引:2,自引:0,他引:2  
Two-phase, immiscible, incompressible flow in porous media is governed by a system of nonlinear partial differential equations. In most practical applications convection physically dominates diffusion, and the object of this paper is to develop a finite difference method combined with the method of characteristics and the lumped mass method to treat the parabolic equation of the differential system. This method is shown satisfy the maximum principle and its error analysis is presented.  相似文献   

8.
This paper proposes a new method for the construction of Bernstein-Bézier algebraic hypersurface on a simplex with prescribed topology.The method is based on the combinatorial patchworking of Viro method.The topology of the Viro Bernstein-Bézier algebraic hypersurface piece is also described.  相似文献   

9.
Composite penalty method of a low order anisotropic nonconforming quadrilateral finite element for the Stokes problem is presented. This method with a large penalty parameter can achieve the same accuracy as the stand method with a small penalty parameter and the convergence rate of this method is two times as that of the standard method under the condition of the same order penalty parameter. The superconvergence for velocity is established as well. The results of this paper are also valid to the most of the known nonconforming finite element methods.  相似文献   

10.
A QP FREE FEASIBLE METHOD   总被引:22,自引:0,他引:22  
In [12], a QP free feasible method was proposed for the minimization of a smooth function subject to smooth inequality constraints. This method is based on the solutions of linear systems of equations, the reformulation of the KKT optimality conditions by using the Fischer-Burmeister NCP function. This method ensures the feasibility of all iterations. In this paper, we modify the method in [12] slightly to obtain the local convergence under some weaker conditions. In particular, this method is implementable and globally convergent without assuming the linear independence of the gradients of active constrained functions and the uniformly positive definiteness of the submatrix obtained by the Newton or Quasi Newton methods. We also prove that the method has superlinear convergence rate under some mild conditions. Some preliminary numerical results indicate that this new QP free feasible method is quite promising.  相似文献   

11.
本文给出并论证了当 n阶实方阵 A具有 r( 1≤ r≤n)个模最大的特征值及其相应特征向量的方法 .实施规范化措施 ,使得行范数等于 1 ,在电子计算机上不会产生溢出停机 ,这是一种有实用价值的算法  相似文献   

12.
《Optimization》2012,61(4-5):363-378
This article presents a comparative analysis of two methods of global optimization: the simulated annealing method and a method based on a combination of the cutting angle method and a local search. This analysis is carried out using results of numerical experiments. These results demonstrate that the combined method is more effective than the simulated annealing method.  相似文献   

13.
提出了一种寻找变系数非线性方程精确解的新方法—相容方程法,利用该方法求出了变系数非线性KP方程的精确解,从而证明了这种方法是十分有效的.  相似文献   

14.
A relaxed version of Karmarkar's method is developed. This method is proved to have the same polynomial time complexity as Karmarkar's method and its efficient implementation using inexact projections is discussed. Computational results obtained using a preliminary implementation of the method are presented which indicate that the method is practicable.This research was supported in part by NSF Grants CDR 84-21402 and DMS-85-12277 and ONR Contract N00014-87-K-0214.  相似文献   

15.
A block version of the Shake method for heavy atom simulation in biological systems is presented in this paper. The method solves successively, independent blocks of constraints of small size by a Newton method. This algorithm is implemented in TAKAKAW, an efficient parallel molecular dynamics code. This method has been tested on a small system and on an ionic canal of 67671 atoms. This revised version was published online in June 2006 with corrections to the Cover Date.  相似文献   

16.
The first-integral method is a direct algebraic method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. This method is based on the theory of commutative algebra. In this work, we apply the first-integral method to study the exact solutions of the Eckhaus equation.  相似文献   

17.
线性不等式组 Ax≤b 的一种新的构造性解法   总被引:1,自引:0,他引:1  
在本文之前,求解 Ax≤b 形成系统理论的解法有两种,第一种是 Fourier-Motzkin方法,第二种是可行方向法.本文提出一种全新的构造型解法,引进了特征矢量、特征表等新概念,本质性地刻划了 Ax≤b 解集的性质,创造了“切割”迭代和表上作业法,充分反映了“切割”迭代的几何背景.  相似文献   

18.
In this paper we design an approximation method for solving stochastic programs with complete recourse and nonlinear deterministic constraints. This method is obtained by combining approximation method and Lagrange multiplier algorithm of Bertsekas type. Thus this method has the advantages of both the two.This project is supported by the National Natural Science Foundation of China.  相似文献   

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