Gradient based and least squares based iterative algorithms for matrix equations AXB + CXD = F

This paper develops a gradient based and a least squares based iterative algorithms for solving matrix equation AXB + CX^TD = F. The basic idea is to decompose the matrix equation (system) under consideration into two subsystems by applying the hierarchical identification principle and to derive the iterative algorithms by extending the iterative methods for solving Ax = b and AXB = F. The analysis shows that when the matrix equation has a unique solution (under the sense of least squares), the iterative solution converges to the exact solution for any initial values. A numerical example verifies the proposed theorems.     

强(A,η)-增生算子及其在变分包含中的应用

本文引入一类广义增生算子——强(A,η)-增生算子.定义强(A,η)-增生算子的广义预解算子并证明它的Lipschitz连续性,进一步证明含强(A,η)-增生算子的变分包含的一些新的迭代算法的收敛性.所得结果改进和推广了许多文献的相应结果.     

最小风险证券组合的结构分析和迭代算法

本文分析了最小风险组合证券投资的结构特征，并提出了一种组合证券风险最小化的迭代算法，证明了其收敛性．该算法操作简单，且易于处理不允许卖空情况下的证券组合问题．     

关于离散HJB方程的下解与上解

本文讨论HJB方程上、下解的几个性质,并讨论了从上解出发的一个迭代法的收敛性.     

An Extension of Least Angle Regression Based on the Information Geometry of Dually Flat Spaces

We extend the least angle regression algorithm using the information geometry of dually flat spaces. The extended least angle regression algorithm is used for estimating parameters in generalized linear regression, and it can be also used for selecting explanatory variables. We use the fact that a model manifold of an exponential family is a dually flat space. In estimating parameters, curves corresponding to bisectors in the Euclidean space play an important role. Originally, the least angle regression algorithm is used for estimating parameters and selecting explanatory variables in linear regression. It is an efficient algorithm in the sense that the number of iterations is the same as the number of explanatory variables. We extend the algorithm while keeping this efficiency. However, the extended least angle regression algorithm differs significantly from the original algorithm. The extended least angle regression algorithm reduces one explanatory variable in each iteration while the original algorithm increases one explanatory variable in each iteration. We show results of the extended least angle regression algorithm for two types of datasets. The behavior of the extended least angle regression algorithm is shown. Especially, estimates of parameters become smaller and smaller, and vanish in turn.     

Iterative solutions to the extended Sylvester-conjugate matrix equations

This paper is concerned with iterative solutions to a class of complex matrix equations. By applying the hierarchical identification principle, an iterative algorithm is constructed to solve this class of complex matrix equations. The range of the convergence factor is given to guarantee that the proposed algorithm is convergent for arbitrary initial matrix by applying a real representation of a complex matrix as a tool. By using some properties of the real representation, a sufficient convergence condition that is easier to compute is also given by original coefficient matrices. Two numerical examples are given to illustrate the effectiveness of the proposed methods.     

Banach空间的上带松弛共强制的广义隐式变分包含组

本文在Banach空间上引入和研究了一类带松弛共强制的广义隐式变分包含组（SNSIVI）．使用M增值算子的预解算子技术，我们构造了一类新的迭代算法逼近这类隐式变分包含组，且在q-一致平滑Banach空间上证明了这类迭代算法的收敛性．我们的结果推广和改进了最近的相关工作．     

Banach空间中广义集值变分包含问题的迭代解

本文研究Banach空间中一类广义集值变分包含问题 ,建立了广义集值变分包含问题的迭代解的一些算法 ,并统一和推广了一些最新文献中的结果 .     

利用波长调制光谱技术测量高温环境中的气体压强、温度和H_2O组分浓度

利用基于可调谐半导体激光器的扫描波长调制光谱技术,实现了高温燃烧场内气体参数的测量。提出了基于迭代算法实现气体压强、温度和组分浓度同时测量的方法,迭代算法具有收敛速度快以及对初始值不敏感等优点。采用频分复用技术,利用两条H_2O吸收谱线(7 454.45和6 806.03cm-1)的谐波信号,对高温燃烧场进行了实验研究,并将气体压强、温度和H_2O组分浓度测量结果与压力传感器、热电偶和直接吸收光谱法的测量结果进行比较,结果表明,基于波长调制光谱技术测得的气体压强、温度和H_2O浓度与预测值基本符合,最大偏差分别在7.6%,8.1%和7.5%以内。此方法具有多参数同时测量、免标定等显著优势,但由于依赖的参数较多,容易对测量精度造成影响。     

非线性体效应的逆问题

非线性体效应在计算机断层扫描重构的理论与应用中,仍然是一个悬而未决的问题。本文利用优化重构算法来解决非线性体效应,建立了离散非线性X射线投影变换模型,将X射线投影变换的逆问题变为一个非凸的优化问题,通过裁剪原用于求解凸优化问题的一阶原对偶算法,提出非线性迭代重构算法来解决非凸问题。通过构建成像系统模型对算法的收敛性和重构精度进行了模拟验证,模拟中重建的图像首先通过检验在极窄的显示窗口中显示小于1%的对比度,然后使用相对于真实图像的差异的l2范数进行定量分析。模拟结果表明,在计算精度范围内,非线性重构算法可以收敛到真实图像,而且对于图像衬度小于1%的细节,重构图像也可以显示出来。该研究结果可为设计有效补偿非线性体效应伪影的计算机断层扫描成像应用算法提供参考。