LPNN-based approach for LASSO problem via a sequence of regularized minimizations

In compressive sampling theory, the least absolute shrinkage and selection operator (LASSO) is a representative problem. Nevertheless, the non-differentiable constraint impedes the use of Lagrange programming neural networks (LPNNs). We present in this article the -LPNN model, a novel algorithm that tackles the LASSO minimization together with the underlying theory support. First, we design a sequence of smooth constrained optimization problems, by introducing a convenient differentiable approximation to the non-differentiable -norm constraint. Next, we prove that the optimal solutions of the regularized intermediate problems converge to the optimal sparse signal for the LASSO. Then, for every regularized problem from the sequence, the -LPNN dynamic model is derived, and the asymptotic stability of its equilibrium state is established as well. Finally, numerical simulations are carried out to compare the performance of the proposed -LPNN algorithm with both the LASSO-LPNN model and a standard digital method.     

带参数的一阶脉冲微分方程边值问题

利用上下解和单调迭代法。讨论了带参数的一阶脉冲微分方程。获得了单边Lipschitz条件下这类方程边值问题的解的存在性。     

利用框架理论对信号进行重建

在Hilbert空间中讨论了框架的一些重要的性质,定义了一个框架算子,并讨论了该算子的性质。根据实际问题构造了一框架,使信号在此框架下的投影正好为非均匀采样值。给出了一种框架界的估计方法和重建原信号的迭代算法,最后,用仿真验证了此算法的有效性。     

A new iterative order reduction (IOR) method for eigensolutions of large structures

Order reduction is a computationally efficient method to estimate some lowest eigenvalues and the corresponding eigenvectors of large structural systems by reducing the order of the original model to a smaller one. But its accuracy is limited to a small range of frequencies that depends on the selection of the retained degrees of freedom. This paper proposes a new iterative order reduction (IOR) technique to obtain accurately the eigensolutions of large structural systems. The technique retains all the inertia terms associated with the removed degrees of freedom. This hence leads to the reduced mass matrix being in an iterated form and the reduced stiffness matrix constant. From these mass and stiffness matrices, the eigensolutions of the reduced system can be obtained iteratively. On convergence the reduced system reproduces the eigensolutions of the original structure. A proof of the convergence property is also presented. Applications of the method to a practical GARTEUR structure as well as a plate have demonstrated that the proposed method is comparable to the commonly used Subspace Iteration method in terms of numerical accuracy. Moreover, it has been found that the proposed method is computationally more efficient than the Subspace Iteration method. Copyright © 2003 John Wiley & Sons, Ltd.     

一种改善Turbo乘积编码OFDM系统性能的新方法

本文提出一种利用对译码器软信息限幅来改善多径衰落信道中Turbo乘积编码OFDM(TPC-OFDM)系统性能的新方法。通过对不同多径衰落信道中QPSK映射和16QAM映射的TPC-OFDM系统性能的数值仿真，结果表明在10^-5误比特率下，这种新方法比传统的迭代译码大约有6～10dB的改进，对严重多径环境下TPC-OFDM系统的错误平底也有明显的改进。     

A Modified Variational-Gradient Method for Quasilinear Equations

A modified variational-gradient method is proposed and substantiated for quasilinear operator equations in a Hilbert space.     

输入——输出迭代算法中松弛因子的确定

本文利用变分的手段提示了输入—输出迭代算法中松弛因子的取值规律。     

Iterative finite element model of nonlinear viscoplastic analyses for blended granular porous media

The iterative finite element model, in which an element is used to represent a single particle, is generated to analyze the global behavior of multiple-material aggregates of materially nonlinear viscoplastic particles. The generalized Maxwell model is used to define four types of specific nonlinear viscoplastic materials, which are the elasto visco-plastic matter with linear viscosity, the plasto visco-plastic material with linear viscosity, the elasto visco-plastic media with nonlinear viscosity, and the plasto visco-plastic media with nonlinear viscosity. The theory and relevant penalty iterative algorithm are developed to analyze the four representative mixed granular systems consisting of materially nonlinear viscous particles. To verify precision of stress calculation, solutions of an axis-symmetric radial flow problem are compared with results of the literature and they are in a great agreement. The results present here provide significant insight into the fundamental behavior of granular media under compaction conditions, including prediction of the overall aggregates stress-strain response.     

SPECTRAL DENSITY ESTIMATION FROM NONLINEARLY OBSERVED DATA

Abstract. The estimation of the spectral density function of a stationary Gaussian process at the input of an instantaneous nonlinearity is considered when the nonlinearity is known and a finite set of observations of the output process is given. A class of spectral estimates is considered and their quadratic-mean consistency is established; precise asymptotic expressions for their bias and covariance are derived and their asymptotic normality is obtained.     

Convergence of iterated boolean sums of simultaneous approximants

Explicit error estimates are given for the iterated Boolean sum of a sequence of simultaneous approximants; the rate of convergence is shown to be improved for smooth functions. The general results are applied in the case of the Bernstein, Durrmeyer and Stancu operators.