Computing orthogonal polynomials on a triangle by degree raising

We give an algorithm for computing orthogonal polynomials over triangular domains in Bernstein–Bézier form which uses only the operator of degree raising and its adjoint. This completely avoids the need to choose an orthogonal basis (or tight frame) for the orthogonal polynomials of a given degree, and hence the difficulties inherent in that approach. The results are valid for Jacobi polynomials on a simplex, and show the close relationship between the Bernstein form of Jacobi polynomials, Hahn polynomials and degree raising.     

增强假设变形梯度有限元方法稳定性计算

讨论了非协调增强假设变形梯度有限元的基本理论、所采用的本构关系和有限元列式.为了克服原先由Simo建议的方法中所固有的缺陷,即在模拟压缩变形时容易出现奇异能量模式而导致计算失稳甚至崩溃,对原方法中有关内变量和应力更新算法进行了改进.计算结果表明,改进的方法在模拟压缩和拉伸模型时,具有较好的计算稳定性.     

部分线性变系数模型中估计的渐进正态性

作为部分线性模型与变系数模型的推广,部分线性变系数模型是一类应用非常广泛的模型,本文基于Profile最小二乘方法给出了模型中参数分量与非参数分量的估计,并在异方差情形下证明了这些估计的渐进正态性.     

实物测量造型中光顺准则和方法探讨

从计算机辅助几何设计（ＣＡＧＤ）中光顺的概念和准则出发，分析了实物测量造型中光顺的特点以及造成不光顺曲线曲面的原因，提出了实物测量造型中光顺的准则，并从技术测量和工艺角度提出了最小二乘法与测绘圆整法．它们是解决实物测量造型中光顺问题的切实可行的方法     

Practical selection of neighbourhoods for local regression in the bivariate case

The use of supports that are variable in shape and size are considered here, in dimension two, for a weighted local average of the data measured on a grid. The possibilities of capturing local features of the function with local methods are explored. Such a scheme is in line with the approximation schemes with parameters regulated adaptively to the data.     

快速付里叶变换在俄歇电子能谱数据分析中的应用

本文讨论用快速付里叶变换法对俄歇直接谱进行反褶积和光顺处理,进而弥补常规仪器分辨率或信噪比的不够.在频域采用“慢截止”方式抑制高次谐波,有效地控制了反褶积结果的发散和寄生振荡的产生.此反褶积方法能明显地提高谱图的分辨率,并同时使曲线光顺.作为实例,对一系列部分氧化的铝试样进行了实验测试和数据处理.     

A smoothing spline based test of model adequacy in polynomial regression

For the regression model % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEamaaBa% aajeaWbaGaamyAaaWcbeaakiabeccaGiabg2da9iabeccaGiaabAga% caGGOaGaamiDamaaBaaajeaWbaGaamyAaaWcbeaakiaacMcacaqGGa% Gaey4kaSIaaeiiamaavababeqcbaCaaiaadMgaaSqab0qaaiabew7a% LbaakiaabccacaGGOaGaeqyTduMaai4jaiaadohacaqGGaGaamyAai% aadMgacaWGKbGaaeiiaiaad6eacaGGOaGaam4taiaacYcacaqGGaGa% eq4Wdm3aaWbaaSqabKqaGgaacaaIYaaaaOGaaiykaiaacMcaaaa!57B9!\[y_i = {\rm{f}}(t_i ){\rm{ }} + {\rm{ }}\mathop \varepsilon \nolimits_i {\rm{ }}(\varepsilon 's{\rm{ }}iid{\rm{ }}N(O,{\rm{ }}\sigma ^2 ))\], it is proposed to test the null hypothesis that f is a polynomial of degree less than some given value m. The alternative is that f is such a polynomial plus a scale factor b ^1/2 times an (m–1)-fold integrated Wiener process. For this problem, it is shown that no uniformly (in b) most powerful test exists, but a locally (at b=0) most powerful test does exist. Derivation and calculation of the test statistic is based on smoothing spline theory. Some approximations of the null distribution of the test statistic for the locally most powerful test are described. An example using real data is shown along with a computing algorithm.This author's research was supported by the National Science Foundation under grants numbered DMS-8202560 and DMS-8603083.     

一类光滑的有理插值公式

本文利用最小二乘法得出了一类光滑的有理插值公式,同时讨论了该公式的一些性质。     

A stochastic framework for recursive computation of spline functions: Part II,smoothing splines

Many of the optimal curve-fitting problems arising in approximation theory have the same structure as certain estimation problems involving random processes. We develop this structural correspondence for the problem of smoothing inaccurate data with splines and show that the smoothing spline is a sample function of a certain linear least-squares estimate. Estimation techniques are then used to derive a recursive algorithm for spline smoothing.     

Efficient algebraic multigrid for migration–diffusion–convection–reaction systems arising in electrochemical simulations

The article discusses components and performance of an algebraic multigrid (AMG) preconditioner for the fully coupled multi-ion transport and reaction model (MITReM) with nonlinear boundary conditions, important for electrochemical modeling. The governing partial differential equations (PDEs) are discretized in space by a combined finite element and residual distribution method. Solution of the discrete system is obtained by means of a Newton-based nonlinear solver, and an AMG-preconditioned BICGSTAB Krylov linear solver. The presented AMG preconditioner is based on so-called point-based classical AMG. The linear solver is compared to a standard direct and several one-level iterative solvers for a range of geometries and chemical systems with scientific and industrial relevance. The results indicate that point-based AMG methods, carefully designed, are an attractive alternative to more commonly employed numerical methods for the simulation of complex electrochemical processes.