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51.
A symbolic algorithm based on the generalized Lucas polynomials of first kind is used in order to compute the Newton sum rules for the zeros of polynomial eigenfunctions of linear differential operators with polynomial coefficients. 相似文献
52.
In this note, we show that a well-known integral method, which was used by Mayne and Polak to compute an -subgradient, can be exploited to compute deterministically an element of the plenary hull of the Clarke generalized Jacobian of a locally Lipschitz mapping regardless of its structure. In particular, we show that, when a locally Lipschitz mapping is piecewise smooth, we are able to compute deterministically an element of the Clarke generalized Jacobian by the adaptive smoothing method. Consequently, we show that the Newton method based on the plenary hull of the Clarke generalized Jacobian can be implemented in a deterministic way for solving Lipschitz nonsmooth equations. 相似文献
53.
Ki Wan Kim Seung Wook Baek 《Journal of Quantitative Spectroscopy & Radiative Transfer》2007,108(3):423-439
An inverse radiation problem was considered to estimate boundary conditions such as temperature distribution and emissivity in axisymmetric absorbing, emitting, and scattering medium, given the measured incident radiative heat fluxes. The finite-volume method was employed to solve a direct radiative transfer equation for a two-dimensional axisymmetric geometry. Various parameter estimators, such as conjugate-gradient method, hybrid genetic algorithm, and finite-difference Newton method, were employed to solve the inverse problems, while discussing their performances in terms of estimation accuracy and computational efficiency. Based on this, we proposed, as a best inverse analysis tool, a new combined method that adopted the hybrid genetic algorithm as an initial value selector and used the finite-difference Newton method as a parameter estimator. 相似文献
54.
55.
In this paper, adaptive finite element method is developed for the estimation of distributed parameter in elliptic equation.
Both upper and lower error bound are derived and used to improve the accuracy by appropriate mesh refinement. An efficient
preconditioned project gradient algorithm is employed to solve the nonlinear least-squares problem arising in the context
of parameter identification problem. The efficiency of our error estimators is demonstrated by some numerical experiments.
相似文献
56.
In this paper, we propose a high order Fourier spectral-discontinuous Galerkin method for time-dependent Schrödinger–Poisson equations in 3-D spaces. The Fourier spectral Galerkin method is used for the two periodic transverse directions and a high order discontinuous Galerkin method for the longitudinal propagation direction. Such a combination results in a diagonal form for the differential operators along the transverse directions and a flexible method to handle the discontinuous potentials present in quantum heterojunction and supperlattice structures. As the derivative matrices are required for various time integration schemes such as the exponential time differencing and Crank Nicholson methods, explicit derivative matrices of the discontinuous Galerkin method of various orders are derived. Numerical results, using the proposed method with various time integration schemes, are provided to validate the method. 相似文献
57.
Shape reconstruction of an inverse boundary value problem of two‐dimensional Navier–Stokes equations
This paper is concerned with the problem of the shape reconstruction of two‐dimensional flows governed by the Navier–Stokes equations. Our objective is to derive a regularized Gauss–Newton method using the corresponding operator equation in which the unknown is the geometric domain. The theoretical foundation for the Gauss–Newton method is given by establishing the differentiability of the initial boundary value problem with respect to the boundary curve in the sense of a domain derivative. The numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
58.
随着现代教育的发展,关注大学生的学习心理研究,提高全体学生的学习效率和效果,教育心理学逐步走入课堂,越来越被教育工作者所重视。许多教师广泛采用教育心理学的原理和理论结构来指导自己的教学实践,并且取得了令人满意的成效。本文采用理论联系实际的方法,对高等教育心理学在牛顿环实验教学中的应用进行了有益探索。 相似文献
59.
We give a Newton type rational interpolation formula (Theorem 2.2). It contains as a special case the original Newton interpolation, as well as the interpolation formula of Liu, which allows to recover many important classical q-series identities. We show in particular that some bibasic identities are a consequence of our formula. 相似文献
60.
B. S. Goh 《Journal of Optimization Theory and Applications》2009,142(2):275-289
We show that, for an unconstrained optimization problem, the long-term optimal trajectory consists of a sequence of greatest
descent directions and a Newton method in the final iteration. The greatest descent direction can be computed approximately
by using a Levenberg-Marquardt like formula. This implies the view that the Newton method approximates a Levenberg-Marquardt
like formula at a finite distance from the minimum point, instead of the standard view that the Levenberg-Marquadt formula
is a way to approximate the Newton method. With the insight gained from this analysis, we develop a two-dimensional version
of a Levenberg-Marquardt like formula. We make use of the two numerically largest components of the gradient vector to define
here new search directions. In this way, we avoid the need of inverting a high-dimensional matrix. This reduces also the storage
requirements for the full Hessian matrix in problems with a large number of variables.
The author thanks Mark Wu, Professors Sanyang Liu, Junmin Li, Shuisheng Zhou and Feng Ye for support and help in this research
as well as the referees for helpful comments. 相似文献