矩阵方程AXB=D的最小二乘Hermite解及其加权最佳逼近

本中,我们讨论了矩阵方程AXB=D的最小二乘Hermite解,通过运用广义奇异值分解(GSVD)，获得了解的通式。此外,对于给定矩阵F，也得到了它的加权最佳逼近表达式。     

A new algorithm for fixed design regression and denoising

In this paper, we present a new algorithm to estimate a regression function in a fixed design regression model, by piecewise (standard and trigonometric) polynomials computed with an automatic choice of the knots of the subdivision and of the degrees of the polynomials on each sub-interval. First we give the theoretical background underlying the method: the theoretical performances of our penalized least-squares estimator are based on non-asymptotic evaluations of a mean-square type risk. Then we explain how the algorithm is built and possibly accelerated (to face the case when the number of observations is great), how the penalty term is chosen and why it contains some constants requiring an empirical calibration. Lastly, a comparison with some well-known or recent wavelet methods is made: this brings out that our algorithm behaves in a very competitive way in term of denoising and of compression.     

Polyparametric modification equation for estimating thermodynamic properties of energetic nitro compounds

Calculation methods, based on hybrid density-functional theory with the basis sets of B3LYP/ 6-311+G (2d, p)//B3LYP/6-31G(d, p)and B3LYP/6-31+G(d)//B3LYP/6-31G(d, p), were applied to determine the thermodynamic characteristics of various energetic nitro compounds. A parametric modification equation and the least-squares approach were used to identify 21 of the energetic research compounds. The atomization energies of these 21 compounds have an average relative error of 0.21–0.25% of the experimental values. The enthalpy (H _f) and the Gibbs energy (G _f) of formation have mean absolute errors of 10.8–11.4 kJ/ mol (2.6–2.7 kcal/mol) and 10.0–10.3 kJ/mol (2.4 kcal/ mol), respectively. The enthalpy and the Gibbs energy of formation obtained exceed those in the literature obtained by semiempirical calculations. The calibrated least-squares parameters and parametric equations were used to predict H _f and G _f for the five newly developed energetic nitro compounds for further applications.Acknowledgements. The authors would like to thank the National Science Council of the Republic of China for financial support of this work under grant no. NSC-91-2113-M-014-003. The National Center for High-Performance Computing providing the computation facility is also acknowledged.     

Inside the Solvency 2 Black Box: Net Asset Values and Solvency Capital Requirements with a least-squares Monte-Carlo approach

The calculation of Net Asset Values and Solvency Capital Requirements in a Solvency 2 context–and the derivation of sensitivity analyses with respect to the main financial and actuarial risk drivers–is a complex procedure at the level of a real company, where it is illusory to be able to rely on closed-form formulas. The most general approach to performing these computations is that of nested simulations. However, this method is also hardly realistic because of its huge computation resources demand. The least-squares Monte Carlo method has recently been suggested as a way to overcome these difficulties. The present paper confirms that using this method is indeed relevant for Solvency 2 computations at the level of a company.     

The numerical solution of the acoustic wave scattering from penetrable obstacles by a least-squares method

This paper documents a numerical method for a two dimensional time-harmonic wave scattering problem by penetrable obstacles. The Fourier–Bessel function combining a multipole expansion is used to give an approximation of the scattering field. This method is based on the least-squares technique. Especially, we find a simple function to control the errors, and then give the theoretical results of the presented method. The continuity across the element boundaries is enforced by minimizing a simple quadratic functional. This method does not need to truncate the domain and could obtain high accuracy by increasing the number of basis functions with even coarse mesh. At last, we give some examples to illustrate the effectiveness of the approach including the solution domain being multiple or even multi-connected.     

Analysis of least-squares mixed finite element methods for nonlinear nonstationary convection-diffusion problems

Some least-squares mixed finite element methods for convection-diffusion problems, steady or nonstationary, are formulated, and convergence of these schemes is analyzed. The main results are that a new optimal a priori error estimate of a least-squares mixed finite element method for a steady convection-diffusion problem is developed and that four fully-discrete least-squares mixed finite element schemes for an initial-boundary value problem of a nonlinear nonstationary convection-diffusion equation are formulated. Also, some systematic theories on convergence of these schemes are established.

     

子孔径拼接技术在大口径高陡度非球面检测中的应用

 为了能够精确地完成对大口径高陡度非球面在细磨和抛光过程中的测量，提出了一种将子孔径拼接技术和补偿技术相结合的检测方法。介绍了该方法的基本原理，建立了合理的数学模型，编制了拼接计算软件。利用该方法对一外形尺寸为400 mm×300 mm的高次离轴非球面进行了测试，通过最小二乘法拟合消去各子孔径相对基准子孔径的调整误差以及整个系统的装调定位误差，得到了准确的全孔径面形分布。对实验精度和误差来源进行了分析，并将拼接面形与全孔径测量面形相对比，二者是一致的。     

速率光纤陀螺寻北仪倾斜补偿算法研究

针对速率光纤陀螺寻北仪,提出了一种倾斜补偿算法.通过采用积分滑动和最小二乘拟合滤波技术,对光纤陀螺和加速度计原始测量信号进行数据处理.试验数据表明,采用本算法解决了由倾斜角存在影响其寻北准确度的关键技术问题.同时给出了提高光纤陀螺寻北仪的准确度的可能因素.     

Bootstrap tests for unit roots in seasonal autoregressive models

This paper proposes bootstrap tests for the presence of unit roots in a seasonal autoregressive model. The asymptotic validity of the proposed bootstrap scheme is established, and Monte Carlo experiments are used to investigate the small-sample performance of the tests.     

Adaptive finite element methods for the identification of distributed parameters in elliptic equation

In this paper, adaptive finite element method is developed for the estimation of distributed parameter in elliptic equation. Both upper and lower error bound are derived and used to improve the accuracy by appropriate mesh refinement. An efficient preconditioned project gradient algorithm is employed to solve the nonlinear least-squares problem arising in the context of parameter identification problem. The efficiency of our error estimators is demonstrated by some numerical experiments.