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931.
Based on radial basis functions approximation, we develop in this paper a new com-putational algorithm for numerical differentiation.
Under an a priori and an a posteriori choice rules for the regularization parameter, we also give a proof on the convergence error estimate in reconstructing the
unknown partial derivatives from scattered noisy data in multi-dimension. Numerical examples verify that the proposed regularization
strategy with the a posteriori choice rule is effective and stable to solve the numerical differential problem.
*The work described in this paper was partially supported by a grant from CityU (Project No. 7001646) and partially supported
by the National Natural Science Foundation of China (No. 10571079). 相似文献
932.
Retrieval of polymeric emulsions Particle Size Distribution (PSD) from Elastic Light Scattering (ELS) measurements requires the solution of an ill conditioned inverse problem. In this paper we compare the performance of classical regularization methods such as Truncated Singular Value Decomposition and Tikhonov's, to a regularization technique due to Pike that includes positivity constraints on the PSD. We also propose a new method that combines Tikhonov's approach with Pike's method. Simulated ELS measurements for two polymeric materials were generated under different experimental noise assumptions. Uncertainties on the polymer refractive index value were also considered. The PSD estimations obtained show that the implementation of the proposed more sophisticated algorithm is convenient for this very ill‐conditioned problem. 相似文献
933.
In this paper, we provide sufficient conditions for the existence of at least three solutions to a three-point boundary value problem for higher-order ordinary differential equations. The nonlinear term f in the differential equation under consideration may depend on higher-order derivatives of arbitrary order and this is where the main novelty of this work lies. By applying the two pairs of upper and lower solutions method of Henderson and Thompson, as well as degree theory, the existence of at least three solutions of the problem is given. 相似文献
934.
Lai-Jiu Lin Qamrul Hasan Ansari Yu-Jen Huang 《Mathematical Methods of Operations Research》2007,65(1):85-98
In this paper, we consider more general forms of generalized vector quasi-equilibrium problems for multivalued maps which
include many known vector quasi-equilibrium problems and generalized vector quasi-variational inequality problems as special
cases. We establish some existence results for solutions of these problems under pseudomonotonicity and u-hemicontinuity/ℓ-hemicontinuity assumptions.
相似文献
935.
936.
本文用二维粒子模拟方法研究了超强超短脉冲激光与圆形等离子体薄靶相互作用中产生的高能离子.模拟研究结果表明,在圆形等离子体薄靶后表面所产生的高能离子,角分布较小,定向性好,能获得很高的能量,并且等离子体薄靶的形状对高能离子的产生和会聚有一定地影响. 相似文献
937.
S. G. Solodky 《Journal of Optimization Theory and Applications》2007,132(1):21-39
An adaptive discretization scheme of ill-posed problems is used for the nonstationary iterated Tikhonov regularization. It
is shown that, for some classes of operator equations of the first kind, the proposed algorithm is more efficient compared
with standard methods.
Communicated by F. A. Potra
This work was partially supported by DAAD under Grant A/01/06016 相似文献
938.
Vera Roshchina 《Journal of Mathematical Analysis and Applications》2007,334(1):261-272
In this paper we establish a relationship between the basic subdifferential and upper exhausters of positively homogeneous and polyhedral functions. In the case of a finite exhauster this relationship is represented in a form of an equality, and in the case of a Lipschitz function an inclusion formula is obtained. 相似文献
939.
In this paper, the equivalence between variational inclusions and a generalized type of Weiner–Hopf equation is established. This equivalence is then used to suggest and analyze iterative methods in order to find a zero of the sum of two maximal monotone operators. Special attention is given to the case where one of the operators is Lipschitz continuous and either is strongly monotone or satisfies the Dunn property. Moreover, when the problem has a nonempty solution set, a fixed-point procedure is proposed and its convergence is established provided that the Brézis–Crandall–Pazy condition holds true. More precisely, it is shown that this allows reaching the element of minimal norm of the solution set. 相似文献
940.
A sufficient optimality criterion for linearly-constrained concave minimization problems is given in this paper. Our optimality criterion is based on the sensitivity analysis of the relaxed linear programming problem. The main result is similar to that of Phillips and Rosen (Ref. 1); however, our proofs are simpler and constructive.In the Phillips and Rosen paper (Ref. 1), they derived a sufficient optimality criterion for a slightly different linearly-constrained concave minimization problem using exponentially many linear programming problems. We introduce special test points and, using these for several cases, we are able to show optimality of the current basic solution.The sufficient optimality criterion described in this paper can be used as a stopping criterion for branch-and-bound algorithms developed for linearly-constrained concave minimization problems.This research was supported by a Bolyai János Research Fellowship BO/00334/00 of the Hungarian Academy of Science and by the Hungarian Scientific Research Foundation, Grant OTKA T038027. 相似文献