Three-Step Predictor-Corrector of Exponential Fitting Method for Nonlinear Schroedinger Equations

We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.     

关于振动模态参数识别的注记

回顾了关于整体拟合的分母多项式系数的争议,论证了Richardson文献中所提供的参数精度不高的原因并非源于Richardson的错误.指出一个经典考核算例的仿真传递函数生成公式不同于复模态理论提供的公式,讨论了两者之间的关系.表1,参9.     

SrFCl:Eu~(2+)晶体的电子自旋共振谱研究

用程序降温法生长了SrFCl:Eu~(2+)晶体,并测量了它的电子自旋共振谱。应用最小二乘法拟合技术对g因子及自旋哈密顿参数进行了精确拟合。报道了各向异性的g因子及有关自旋哈密顿参量。发现并归属了Eu~(2+)的高阶禁阻跃迁。     

LabVIEW在曲线拟合中的应用研究

介绍了LabVIEW中用于曲线拟合的子模块，对各子模块的曲线拟合理论作了介绍，重点介绍了非线性Lev-Mar拟合理论，并以例子辅助说明．     

Local polynomial fitting under association

We consider the estimation of multivariate regression functions r(x₁,…,x_d) and their partial derivatives up to a total order p1 using high-order local polynomial fitting. The processes {Y_i,X_i} are assumed to be (jointly) associated. Joint asymptotic normality is established for the estimates of the regression function r and all its partial derivatives up to the total order p. Expressions for the bias and variance/covariance matrix (of the asymptotic distribution) are given.     

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.     

学生成绩分布与一种简便的评估试卷命题质量的方法

利用统计分析方法，对辽宁师范大理科学生成绩分布情况进行了分析；给出了一种评估试卷命题质量的简便易行的方法一用正态曲线拟合的方法，实际证明，效果很好。     

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     

Linear least squares problems with data over incomplete grids

The paper addresses bivariate surface fitting problems, where data points lie on the vertices of a rectangular grid. Efficient and stable algorithms can be found in the literature to solve such problems. If data values are missing at some grid points, there exists a computational method for finding a least squares spline by fixing appropriate values for the missing data. We extended this technique to arbitrary least squares problems as well as to linear least squares problems with linear equality constraints. Numerical examples are given to show the effectiveness of the technique presented. AMS subject classification (2000)  65D05, 65D07, 65D10, 65F05, 65F20     

几种基于散乱数据拟合的局部插值方法

本文首先针对散乱数据拟合的Shepard方法,结合截断多项式、B样条基函数和指数函数来构造其权函数,使新的权函数具有更高的光滑度和更好的衰减性,并且其光滑性和衰减性可以根据实际需要自由调节,从而提高了曲面的拟合质量．同时还给出一种类似的局部插值方法．另外,本文还基于多重二次插值,结合多元样条的思想,给出了两个局部插值算法．该算法较好地继承了多重二次插值曲面的性质,从而保证了拟合曲面具有好地光顺性和拟合精度．曲面整体也具有较高的光滑性．