彩色打印机特性化多元回归模型的研究

多元回归法是彩色打印机特性化普遍采用的方法,实验对影响多元回归精度的阶数、色空间选择、以及训练样本选取进行了研究.研究结果表明:(1)二、三、四阶的特性化精度分别在10.9±0.3、6.6±0.2、6.0±0.2个CIELAB色差单位;(2)回归模型采用RGB到CIELAB或CIEXYZ的预测精度基本相同,大概相差1个...     

随机对流扩散方程的数值仿真

本文针对对流一扩散随机过程在随机输入（即随机输运和源项）,作用下进行数值仿真。我们先将对流扩散随机微分方程中的随机函数采用有限项截断的多项式浑沌展开（Polynomial Chaos Expansion）展开,再由Galerkin映射法得到求解浑沌展开系数的确定性方程组。这是一个在物理空间包含多尺度解的大方程组。为此我...     

Accurate estimation of solvation free energy using polynomial fitting techniques

This report details an approach to improve the accuracy of free energy difference estimates using thermodynamic integration data (slope of the free energy with respect to the switching variable λ) and its application to calculating solvation free energy. The central idea is to utilize polynomial fitting schemes to approximate the thermodynamic integration data to improve the accuracy of the free energy difference estimates. Previously, we introduced the use of polynomial regression technique to fit thermodynamic integration data (Shyu and Ytreberg, J Comput Chem, 2009, 30, 2297). In this report we introduce polynomial and spline interpolation techniques. Two systems with analytically solvable relative free energies are used to test the accuracy of the interpolation approach. We also use both interpolation and regression methods to determine a small molecule solvation free energy. Our simulations show that, using such polynomial techniques and nonequidistant λ values, the solvation free energy can be estimated with high accuracy without using soft‐core scaling and separate simulations for Lennard‐Jones and partial charges. The results from our study suggest that these polynomial techniques, especially with use of nonequidistant λ values, improve the accuracy for ΔF estimates without demanding additional simulations. We also provide general guidelines for use of polynomial fitting to estimate free energy. To allow researchers to immediately utilize these methods, free software and documentation is provided via http://www.phys.uidaho.edu/ytreberg/software . © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

FAST OPTIMIZATION METHOD OF REENTRY TRAJECTORY CONSIDERING AERODYNAMIC PARAMETER PERTURBATION

针对传统再入轨迹优化方法收敛速度慢、对初值敏感程度高等的局限性,提出了一种基于序列凸优化的再入轨迹快速求解方法.该方法以倾侧角的变化率作为控制量,改进了现有凸化策略,考虑到抑制数值优化过程中由于数值离散方式带来的锯齿化现象,采用 B 样条曲线离散控制量,同时为避免算法在初始猜想值附近出现伪不可行的问题,增加额外虚拟控制量,通过一种"回溯直线"搜索的方法,提高算法的稳定性、快速性和寻优结果的光滑性.为研究飞行器再入过程中的气动参数扰动问题,采用采样点少、易于实现,计算效率高的广义混沌多项式理论研究方法,建立了基于广义混沌多项式和凸优化相结合的再入轨迹鲁棒优化模型,该模型在优化过程中考虑气动参数扰动对寻优结果的影响作用,避免了传统轨迹与制导律的复杂迭代设计环节,可有效降低优化轨迹对气动参数扰动的敏感程度,在气动参数不确定条件的干扰下,依然可以保证飞行器顺利安全的完成飞行任务.最后,以美国某可重复使用飞行器的再入任务为例,验证了基于序列凸优化的再入轨迹优化方法的快速性以及鲁棒优化模型对气动参数扰动的抗干扰性能力,表明了该方法具有一定的工程应用性.     

On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems

This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point belongs to the sufficiently small neighbourhood of the solution set. Proposed method could be applied for solving large systems of linear inequalities.     

On some classes of structured matrices with algebraic trigonometric eigenvalues

Diagonal plus semiseparable matrices are constructed, the eigenvalues of which are algebraic numbers expressed by simple closed trigonometric formulas.     

A stabilized formulation for the advection–diffusion equation using the Generalized Finite Element Method

This paper presents a stable formulation for the advection–diffusion equation based on the Generalized (or eXtended) Finite Element Method, GFEM (or X‐FEM). Using enrichment functions that represent the exponential character of the exact solution, smooth numerical solutions are obtained for problems with steep gradients and high Péclet numbers in one‐ and two‐dimensions. In contrast with traditional stabilized methods that require the construction of stability parameters and stabilization terms, the present work avoids numerical instabilities by improving the classical Galerkin solution with enrichment functions (that need not be polynomials) using GFEM, which is an instance of the partition of unity framework. This work also presents a strategy for constructing enrichment functions for problems involving complex geometries by employing a global–local‐type approach. Representative numerical results are presented to illustrate the performance of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Measuring the interactions among variables of functions over the unit hypercube

By considering a least squares approximation of a given square integrable function f:n[0,1]→R by a multilinear polynomial of a specified degree, we define an index which measures the overall interaction among variables of f. This definition extends the concept of Banzhaf interaction index introduced in cooperative game theory. Our approach is partly inspired from multilinear regression analysis, where interactions among the independent variables are taken into consideration. We show that this interaction index has appealing properties which naturally generalize several properties of the Banzhaf interaction index. In particular, we interpret this index as an expected value of the difference quotients of f or, under certain natural conditions on f, as an expected value of the derivatives of f. Finally, we discuss a few applications of the interaction index in aggregation function theory.