Eight-node conforming straight-side quadrilateral element with high-order completeness (QH8-C1)

A new eight-node conforming quadrilateral element with high-order completeness, denoted as QH8-C1, is proposed in this article. First, expressions for the interpolation displacement function satisfying the requirements for high-order completeness in the global coordinate system are constructed. Second, the displacement function expression in global coordinates is transformed into isoparametric coordinates, and the relationships between the two series of coefficients for the two kinds of displacement function expressions are found. Third, the displacement function expression is modified to satisfy the requirements of nodal freedom and interelement boundary continuity. The key to the new element construction is the derivation of the linear relationship expressions among 12 coefficients of element displacement interpolation polynomials in the global and isoparametric coordinate systems. As a result, the relationship between quadratic completeness and interelement continuity is explicitly given, and a proof of the completeness and the continuity was conducted to theoretically guarantee the validity of the derivation results. Furthermore, in order to verify the correctness of the theoretical work, nine numerical examples were performed. The computation results from these examples demonstrate that QH8-C1 exhibited excellent performance, including high simulation accuracy, fast convergence, insensitivity to mesh distortion, and monotonic convergence.     

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.     

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.     

宽线性共轭梯度算法及其在盲多用户检测中的应用

本文提出了一种宽线性共轭梯度算法，分析了算法在均值意义下的收敛性，并给出了算法稳定条件。仿真表明，新算法应用于码分多址系统多址干扰抑制时的性能优于Yin（2003）及Schober（2004）所提出的算法。     

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.     

关于Grünwald型多项式算子的线性组合

研究了Grünwald型多项式算子Hn(f;x,r)对f(x)∈Cj[-1,1],1≤j≤r的逼近阶,在连续状态下给出了点态的逼近阶.