一种有效的新预条件Gauss-Seidel迭代法

为了改善古典迭代法的收敛速度,本文提出一种带参数的新预条件方法,并对参数的选择给出必要条件,证明了对于非奇异不可约M一矩阵,新预条件方法收敛且可以加速Gauss—Seidel迭代法的收敛速度,数值例子表明新预条件方法是有效的．     

On the generalized Hyers-Ulam stability of multi-quadratic mappings

A mapping f:Vⁿ?W, where V is a commutative group, W is a linear space, and n≥2 is an integer, is called multi-quadratic if it is quadratic in each variable. In this paper, we prove the generalized Hyers-Ulam stability of multi-quadratic mappings in Banach spaces and complete non-Archimedean spaces.     

Shape optimization for tumor location

In non-invasive thermal diagnostics, accurate correlations between the thermal image at skin surface and interior human physiology are desired. In this work, an estimation methodology to determine unknown geometrical parameters of an embedded tumor is proposed. We define a functional that represents the mismatch between a measured experimental temperature profile, which may be obtained by infrared thermography on the skin surface, and the solution of an appropriate boundary problem. This functional is related to the geometrical parameters through the solution of the boundary problem, in such a way that finding the minimum of this functional form also means finding the unknown geometrical parameters of the embedded tumor. Sensitivity analysis techniques coupled with the adjoint method were considered to compute the shape derivative of the functional. Then, a nonmonotone spectral projected gradient method was implemented to solve the optimization problem of finding the optimal geometric parameters.     

Space and time localization for the estimation of distributed parameters in a finite element model

In this paper we study the problem of estimating the possibly non-homogeneous material coefficients inside a physical system, from transient excitations and measurements made in a few points on the boundary. We assume there is available an adequate Finite Element (FEM) model of the system, whose distributed physical parameters must be estimated from the experimental data.We propose a space–time localization approach that gives a better conditioned estimation problem, without the need of an expensive regularization. Some experimental results obtained on an elastic system with random coefficients are given.     

Controlling the diffusionless Lorenz equations with periodic parametric perturbation

Diffusionless Lorenz equations (DLE) are a simple one-parameter version of the well-known Lorenz model, which was obtained in the limit of high Rayleigh and Prandtl numbers, physically corresponding to diffusionless convection. A simple control method is presented to control chaos by using periodic parameter perturbation in DLE. By using the generalized Melnikov method, the parameter conditions could be obtained to guide the controlled DLE to a low-periodic motion. Moreover, the existence conditions of periodic orbits and homoclinic orbits in the system are given. Some results of the numerical simulation are also explained clearly by a rigorous analysis.     

A hybrid multi-criteria decision-making model for firms competence evaluation

In this paper, we present a hybrid multi-criteria decision-making (MCDM) model to evaluate the competence of the firms. According to the competence-based theory reveals that firm competencies are recognized from exclusive and unique capabilities that each firm enjoy in marketplace and are tightly intertwined within different business functions throughout the company. Therefore, competence in the firm is a composite of various attributes. Among them many intangible and tangible attributes are difficult to measure. In order to overcome the issue, we invite fuzzy set theory into the measurement of performance. In this paper first we calculate the weight of each criterion through adaptive analytic hierarchy process (AHP) approach (A³) method, and then we appraise the performance of firms via linguistic variables which are expressed as trapezoidal fuzzy numbers. In the next step we transform these fuzzy numbers into interval data by means of α-cut. Then considering different values for α we rank the firms through TOPSIS method with interval data. Since there are different ranks for different α values, we apply linear assignment method to obtain final rank for alternatives.     

基于贝叶斯最大化后验估计方法的图片合成模型研究

在图像处理应用中,常常需要根据一些列相关的输入图片生成一张新的图片。现有的研究大都设定一些启发式规则用于图片的合成过程。为了提高图片合成的性能,提出了一种基于改进的贝叶斯方法的图片合成模型。在给定理想的图片合成模型后,对传感器误差和图片误差进行了分析。由于图片误差和几何误差之间是相关的,因此分析了它们之间的关系。在根据已有数据对模型进行后验估计时,通过最小化能量来得到模型的先验参数。在目标函数的优化过程中,基于现有研究通过重新赋权值的迭代方法进行优化问题的求解。最后,通过大量的实验表明,所提出的图片合成模型与相关方法相比具有更好的图片合成和渲染效果。     

A kernel-based centroid classifier using hypothesis margin

The centroid-based classifier is both effective and efficient for document classification. However, it suffers from over-fitting and linear inseparability problems caused by its fundamental assumptions. To address these problems, we propose a kernel-based hypothesis margin centroid classifier (KHCC). First, KHCC optimises the class centroids via minimising hypothesis margin under structural risk minimisation principle; second, KHCC uses the kernel method to relieve the problem of linear inseparability in the original feature space. Given the radial basis function, we further discuss a guideline for tuning the value of its parameter. The experimental results on four well-known data-sets indicate that our KHCC algorithm outperforms the state-of-the-art algorithms, especially for the unbalanced data-set.     

Self-consistent gradient flow for shape optimization

We present a model for image segmentation and describe a gradient-descent method for level-set based shape optimization. It is commonly known that gradient-descent methods converge slowly due to zig–zag movement. This can also be observed for our problem, especially when sharp edges are present in the image. We interpret this in our specific context to gain a better understanding of the involved difficulties. One way to overcome slow convergence is the use of second-order methods. For our situation, they require derivatives of the potentially noisy image data and are thus undesirable. Hence, we propose a new method that can be interpreted as a self-consistent gradient flow and does not need any derivatives of the image data. It works very well in practice and leads to a far more efficient optimization algorithm. A related idea can also be used to describe the mean-curvature flow of a mean-convex surface. For this, we formulate a mean-curvature Eikonal equation, which allows a numerical propagation of the mean-curvature flow of a surface without explicit time stepping.