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971.
In this article, approximate solutions of multi-objective optimization problems are analysed. The notion of approximate solution suggested by Kutateladze is dealt with, and, utilizing different scalarization approaches, some necessary and sufficient conditions for ?-(strong, weak, proper) efficiency are provided. Almost all of the provided results are established without any convexity assumption. 相似文献
972.
973.
针对研究吊桥模型而建立的四阶微积分方程, 提出Legendre谱逼近法进行求解.构造迭代算法来求解得到的线性系统, 证明了迭代格式的收敛性, 对问题进行了误差分析.数值算例验证了迭代的收敛性和方法的高精度. 相似文献
974.
Steffen Roch 《Numerical Functional Analysis & Optimization》2013,34(1-2):241-253
The paper deals with spectral approximation of Wiener-Hopf operators acting on Lp -spaces by their finite sections. The generating functions of the Wiener-Hopf operators are supposed to be continuous plus almost periodic.While the usual spectra of the finite sections drastically fail to converge to the spectrum of the Wiener-Hopf operator,it turns out that other spectral approximants, viz. the pseudospectra and the numerical ranges, do converge perfectly.The proof requires a modified approach to the finite section method for Wiener-Hopf operators. This note generalizes results obtained by Böttcher, Grudsky and Silbermann for the case of continuous generating functions. 相似文献
975.
The problem of nonlinear dynamical system modeling, considered in this paper, is motivated by restrictions arising in real-world tasks. The restrictions are that first, a system input cannot be entirely observed for one trial. Second, the system model must be subjected to the causality principle. Third, the input is corrupted by noise so that no relationship between the reference input and noise is known. Fourth, the model should have some degrees of freedom so that the associated accuracy can be regulated by a variation of these freedom degrees. We propose and justify new procedures for the nonlinear system modeling that are initialized by these motivations. The models are nonlinear and given by so called r-degree operators that can be reduced to a matrix form presentation. To satisfy the restrictions above, the matrices have special structures that we call the lower p-band matrices. The degree r of the models is the required degree of freedom. The rigorous analysis of errors associated with the presented techniques is given. Numerical experiments with real data demonstrate the efficiency of the proposed approach. 相似文献
976.
H. T. Banks C. J. Musante J. K. Raye 《Numerical Functional Analysis & Optimization》2013,34(7-8):791-816
We present a rigorous theoretical framework for approximation of nonlinear parabolic systems with delays in the context of inverse least squares problems. Convergence of approximate optimal parameters and that of forward solutions in the context of semidiscrete Galerkin schemes are given. Sample numerical results demonstrating the convergence are given for a model of dioxin uptake and elimination in a distributed liver model that is a special case of the general theoretical framework. 相似文献
977.
978.
Regularized versions of continuous analogues of Newton's method and modified Newton's method for obtaining approximate solutions to a nonlinear ill-posed operator equation of the form F(u) = f, where F is a monotone operator defined from a Hilbert space H into itself, have been studied in the literature. For such methods, error estimates are available only under Hölder-type source conditions on the solution. In this paper, presenting the background materials systematically, we derive error estimates under a general source condition. For the special case of the regularized modified Newton's method under a Hölder-type source condition, we also carry out error analysis by replacing the monotonicity of F by a weaker assumption. This analysis facilitates inclusion of certain examples of parameter identification problems, which was not possible otherwise. Moreover, an a priori stopping rule is considered when we have a noisy data f δ instead of f. This rule yields not only convergence of the regularized approximations to the exact solution as the noise level δ tends to zero but also provides convergence rates that are optimal under the source conditions considered. 相似文献
979.
Qiaoluan Helen Li 《Numerical Functional Analysis & Optimization》2013,34(6):641-658
In this article, we consider the problem of proving the optimality of several approximation spaces by means of n-widths. Specifically, they are optimal subspaces for approximating bounded subsets in some Hilbert spaces with mesh-dependent norms. We prove that finite element spaces and newly developed generalized L-spline spaces are optimal subspaces for n-widths. 相似文献
980.
G. Sankara Raju Kosuru P. Veeramani 《Numerical Functional Analysis & Optimization》2013,34(7):821-830
We introduce a notion of pointwise cyclic contraction T satisfying TA ? B and TB ? A to obtain the existence of a point x ∈ A, such that d(x, Tx) = dist(A, B), known as a best proximity point for such a map. We also prove that for any x ∈ A, the Picard iteration {T2nx} converges to a best proximity point. 相似文献