一维搜索的一个Anderson-Bjrck外推加速算法

对一维搜索的二点二次插值法,利用Anderson-B j rck外推的思想提出了一个加速收敛算法,得出并证明了两条收敛性定理,且通过数值试验验证了该算法比二点二次插值法收敛速度快很多。     

A systematic theoretical investigation of the valence excited states of the diatomic molecules B2, C2, N2 and O2

A quantitative survey on the performance of multireference (MR), configuration interaction with all singles and doubles (CISD), MRCISD with the Davidson correction and MR-average quadratic coupled cluster (AQCC) methods for a wide range of excited states of the diatomic molecules B₂, C₂, N₂ and O₂ is presented. The spectroscopic constants r _e, ω_e, T _e and D _e for a total of 60 states have been evaluated and critically compared with available experimental data. Basis set extrapolations and size-extensivity corrections are essential for highly accurate results: MR-AQCC mean-errors of 0.001 ?, 10 cm⁻¹, 300 cm⁻¹ and 300 cm⁻¹ have been obtained for r _e, ω_e, T _e and D _e, respectively. Owing to the very systematic behavior of the results depending on the basis set and the choice of method, shortcomings of the calculations, such as Rydberg state coupling or insufficient configuration spaces, can be identified independently of experimental data. On the other hand, significant discrepancies with experiment for states which indicate no shortcomings whatsoever in the theoretical treatment suggest the re-evaluation of experimental results. The broad variety of states included in our survey and the uniform quality of the results indicate that the observed systematics is a general feature of the methods and, hence, is molecule-independent. Received: 12 June 2000 / Accepted: 1 September 2000 / Published online: 21 December 2000     

无线视频传感阵列低复杂度多视点视频编码方案

基于网络中心节点的运动矢量外推技术,提出了一种无线视频传感阵列的低复杂度多视点视频编码方法。该方法考虑到密集型视频传感阵列各视点间通信复杂、布线繁重、且位于各相机节点内的编码器由于计算能力、功耗等限制难以完成复杂的编码过程等特点,利用运动矢量外推逼近技术将大量的运动估计运算从视频编码端移到了网络中心节点,使得新编解码框架下编码器的运动估计的计算复杂度只有传统全搜索运动估计运算的0.3%,降低了系统传感阵列编码端功耗。实验结果表明,该方法的率失真性能比H.264-I帧高出4 dB以上,接近H.264-P帧编码,优于基于Wyner-Ziv理论的分布式多视点视频编码方法。     

变系数情形下Criss-Cross三角形线性元的渐近展式与超收敛

本文讨论了二阶椭圆方程变系数情形下Criss-Cross三角形线性元的超收敛性质,得到了有限元的渐进展式、外推及高精度组合公式等结果.     

Numerical solution of fractional order differential equations by extrapolation

We present an extrapolation type algorithm for the numerical solution of fractional order differential equations. It is based on the new result that the sequence of approximate solutions of these equations, computed by means of a recently published algorithm by Diethelm [6], possesses an asymptotic expansion with respect to the stepsize. From this we conclude that the application of extrapolation is justified, and we obtain a very efficient differential equation solver with practically no additional numerical costs. This is also illustrated by a number of numerical examples. This revised version was published online in August 2006 with corrections to the Cover Date.     

Optimal designs for minimax extrapolation

Speckman developed a minimax linear estimator robust against departures from an assumed model. Some concomitant questions of optimal design are investigated.     

A comparative study of ADI splitting methods for parabolic equations in two space dimensions

The main purpose of the paper is a numerical comparison of three integration methods for semi-discrete parabolic partial differential equations in two space variables. Linear as well as nonlinear,equations are considered. The integration methods are the well-known ADI method of Peaceman and Rachford, a global extrapolation scheme of the classical ADI method to order four and a fourth order, four-step ADI splitting method.     

Extrapolation of the Hood–Taylor elements for the Stokes problem

An asymptotic error expansion concerning of Hood–Taylor elements for the Stokes problem is established on uniform rectangular meshes. The extrapolation based on such an expansion increases the rate of convergence by one order.     

The extrapolated first order method for solving systems with complex eigenvalues

An extrapolated form of the basic first order stationary iterative method for solving linear systems when the associated iteration matrix possesses complex eigenvalues, is investigated. Sufficient (and necessary) conditions are given such that convergence is assured. An analytic determination of good (and sometimes optimum) values of the involved real parameter is presented in terms of certain bounds on the eigenvalues of the iteration matrix. The usefulness of the developed theory is shown through a simple application to the conventional Jacobi method.     

Counterexamples to the asymptotic expansion of interpolation in finite elements

We present counterexamples to the asymptotic expansion of interpolation in finite element methods for solving differential equations, which was expected to hold in the finite element community.