Iterative regularization methods for atmospheric remote sensing

In this paper we present different inversion algorithms for nonlinear ill-posed problems arising in atmosphere remote sensing. The proposed methods are Landweber's method (LwM), the iteratively regularized Gauss-Newton method, and the conventional and regularizing Levenberg-Marquardt method. In addition, some accelerated LwMs and a technique for smoothing the Levenberg-Marquardt solution are proposed. The numerical performance of the methods is studied by means of simulations. Results are presented for an inverse problem in atmospheric remote sensing, i.e., temperature sounding with an airborne uplooking high-resolution far-infrared spectrometer.     

互补型自适应滤波器在心磁信号处理中的应用

将心磁信号从干扰噪声中加以提取并有效地消除噪声干扰是心磁信号处理中尤为重要的环节 .从改进算法的角度出发，提出互补型自适应滤波器结构以实现心磁信号的消噪处理.该滤波器针对心磁这类非平稳信号进行设计，有效地解决了常规自适应滤波器应用于心磁信号处理时收敛速度和稳态误差的矛盾.通过仿真实验和心磁实验结果表明，该算法能有效地消除心磁信号的背景噪声和工频干扰噪声.同时该算法也可用于其他非平稳信号的消噪处理. 关键词： 自适应滤波 心磁图 最小均方误差     

四种多变量校准方法在FTIR多组分分析中的性能比较

本文对四种多变量校准方法－－经典最小二乘法（CLS），偏最小二乘法（PLS），卡尔曼滤波法（KFM）以及人工神经网络法（ANN）－－在多组分浓度分析方面的性能进行了比较。选择五种红外谱图严重混叠的大气有机毒物－－1，3－丁二烯，苯，邻二甲苯，氯苯和丙烯醛－－作为分析对象。分别计算各种方法对该5组分体系的平均预测误差MPE和平均相对误差MRE进行比较。结果表明，偏最小二乘法在处理这类问题中是最稳健的方法。     

A geometric theory forL 2-stability of the inverse problem in a one-dimensional elliptic equation from anH 1-observation

This study provides a stability theory for the nonlinear least-squares formulation of estimating the diffusion coefficient in a two-point boundary-value problem from an error-corrupted observation of the state variable. It is based on analysing the projection of the observation on the nonconvex attainable set.This research was started while G. Chavent visited the Technical University of Graz. Support through the Steiermaerkische Landesregierung is gratefully acknowledged.     

Bivariate Free Knot Splines

We consider the least squares approximation of gridded 2D data by tensor product splines with free knots. The smoothing functional to be minimized—a generalization of the univariate Schoenberg functional—is chosen in such a way that the solution of the bivariate problem separates into the solution of a sequence of univariate problems in case of fixed knots. The resulting optimization problem is a constrained separable least squares problem with tensor product structure. Based on some ideas developed by the authors for the univariate case, an efficient method for solving the specially structured 2D problem is proposed, analyzed and tested on hand of some examples from the literature.     

偏最小二乘回归的贝叶斯正则化神经网络集成模型在证券分析预测中的应用

神经网络集成技术能有效地提高神经网络的预测精度和泛化能力,已经成为机器学习和神经计算领域的一个研究热点.利用Bagging技术和不同的神经网络算法生成集成个体,并用偏最小二乘回归方法从中提取集成因子,再利用贝叶斯正则化神经网络对其集成,以此建立上证指数预测模型.通过上证指数开、收盘价进行实例分析,计算结果表明该方法预测精度高、稳定性好.     

A note on the complex semi‐definite matrix Procrustes problem

This note outlines an algorithm for solving the complex ‘matrix Procrustes problem’. This is a least‐squares approximation over the cone of positive semi‐definite Hermitian matrices, which has a number of applications in the areas of Optimization, Signal Processing and Control. The work generalizes the method of Allwright (SIAM J. Control Optim. 1988; 26 (3):537–556), who obtained a numerical solution to the real‐valued version of the problem. It is shown that, subject to an appropriate rank assumption, the complex problem can be formulated in a real setting using a matrix‐dilation technique, for which the method of Allwright is applicable. However, this transformation results in an over‐parametrization of the problem and, therefore, convergence to the optimal solution is slow. Here, an alternative algorithm is developed for solving the complex problem, which exploits fully the special structure of the dilated matrix. The advantages of the modified algorithm are demonstrated via a numerical example. Copyright © 2007 John Wiley & Sons, Ltd.     

非线性最小二乘问题的信赖域方法

本文提出一个新的非线性最小二乘的信赖域方法,在该方法中每个信赖域子问题只需要一次求解,而且每次迭代的一维搜索步长因子是给定的,避开一维搜索的环节,大大地提高了算法效率.文中证明了在一定的条件下算法的全局收敛性.     

Assessment of some iterative methods for non-symmetric linear systems arising in computational fluid dynamics

Various tests have been carried out in order to compare the performances of several methods used to solve the non-symmetric linear systems of equations arising from implicit discretizations of CFD problems, namely the scalar advection-diffusion equation and the compressible Euler equations. The iterative schemes under consideration belong to three families of algorithms: relaxation (Jacobi and Gauss-Seidel), gradient and Newton methods. Two gradient methods have been selected: a Krylov subspace iteration method (GMRES) and a non-symmetric extension of the conjugate gradient method (CGS). Finally, a quasi-Newton method has also been considered (Broyden). The aim of this paper is to provide indications of which appears to be the most adequate method according to the particular circumstances as well as to discuss the implementation aspects of each scheme.     

Superconvergence of discontinuous Galerkin finite element method for the stationary Navier‐Stokes equations

This article focuses on discontinuous Galerkin method for the two‐ or three‐dimensional stationary incompressible Navier‐Stokes equations. The velocity field is approximated by discontinuous locally solenoidal finite element, and the pressure is approximated by the standard conforming finite element. Then, superconvergence of nonconforming finite element approximations is applied by using least‐squares surface fitting for the stationary Navier‐Stokes equations. The method ameliorates the two noticeable disadvantages about the given finite element pair. Finally, the superconvergence result is provided under some regular assumptions. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 421–436, 2007