A New Extrapolation Economy Cascadic Multigrid Method for Image Restoration Problems

In this paper, a new extrapolation economy cascadic multigrid method is proposed to solve the image restoration model. The new method combines the new extrapolation formula and quadratic interpolation to design a nonlinear prolongation operator, which provides more accurate initial values for the fine grid level. An edge preserving denoising operator is constructed to remove noise and preserve image edges. The local smoothing operator reduces the influence of staircase effect. The experiment results show that the new method not only improves the computational efficiency but also ensures good recovery quality.

基于Power Extrapolation和Adaptive Method的网页评估新算法

Google的PageRank算法通过对超链接结构的分析,有效地提高了搜索结果的排序质量。PowerExtrapolation算法通过特征值直接求解马尔可夫超链接矩阵的主特征向量,但该算法的迭代次数与参数d的选择密切相关,而参数d的确定目前无明显规律可寻。另一方面,AdaptiveMethod通过将马尔可夫超链接矩阵稀疏化以达到节省迭代时间的目的。文章在PowerExtrapolation算法的基础上引入AdaptiveMethod,实验结果初步证明了新算法可以减少迭代运算的时间。

SnO_2-based solid solutions for CH_4 deep oxidation: Quantifying the lattice capacity of SnO_2 using an X-ray diffraction extrapolation method

A series of SnO2‐based catalysts modified by Mn, Zr, Ti and Pb oxides with a Sn/M （M=Mn, Zr, Ti and Pb） molar ratio of 9/1 were prepared by a co‐precipitation method and used for CH4 and CO oxidation. The Mn3＋, Zr4＋, Ti4＋and Pb4＋cations are incorporated into the lattice of tetragonal rutile SnO2 to form a solid solution structure. As a consequence, the surface area and thermal stability of the catalysts are improved. Moreover, the oxygen species of the modified catalysts become easier to be reduced. Therefore, the oxidation activity over the catalysts was improved, except for the one modified by Pb oxide. Manganese oxide demonstrates the best promotional effects for SnO2. Using an X‐ray diffraction extrapolation method, the lattice capacity of SnO2 for Mn2O3 was 0.135 g Mn2O3/g SnO2, which indicates that to form stable solid solution, only 21%Sn4＋cations in the lattice can be maximally replaced by Mn3＋. If the amount of Mn3＋cations is over the capacity, Mn2O3 will be formed, which is not favorable for the activity of the catalysts. The Sn rich samples with only Sn‐Mn solid solution phase show higher activity than the ones with excess Mn2O3 species.

A SIMPLE PROOF OF STABILITY AND CONVERGENCE IN L＿2 FOR SOME DIFFERENCE SCHEMES AND THEIR EXTRAPOLATION METHOD FOR PARABOLIC EQUATIONS

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Fatigue life evaluation of girth butt weld within welded cast steel joints based on the extrapolation notch stress method

The fatigue life evaluation of the girth butt weld within the welded cast steel joint was studied based on the extrapolation notch stress method.Firstly,the mesh sensitivity of the finite element model of the welded cast steel joint was analyzed to determine the optimal mesh size.Based on the stress field analysis of the finite element model of the welded cast steel joint at the weld toe and weld root,the sharp model of the extrapolation notch stress method was applied to derive the effective notch stress of the rounded model belonging to the effective notch stress method,in which the key problem is to calculate the extrapolation point C,and the extrapolation point C has an exponential function relationship with the geometric parameters of the welded cast steel joint.By setting different values of geometric parameters,the corresponding value of parameter C is calculated,and then the functional relationship between the extrapolation point C and the geometric parameters can be obtained by the multiple linear regression analysis.Meanwhile,the fatigue life evaluation of the girth butt weld within welded cast steel joints based on the effective notch stress was performed according to the guideline recommended by the IIW(International Institute of Welding).The results indicate that the extrapolation notch stress method can effectively simplify the process of calculating the effective notch stress and accurately evaluate the fatigue life of the girth butt weld within welded cast steel joints.

Extrapolation Method for Cauchy Principal Value Integral with Classical Rectangle Rule on Interval

In this paper,the classical composite middle rectangle rule for the computation of Cauchy principal value integral(the singular kernel 1=(x-s))is discussed.With the density function approximated only while the singular kernel is calculated analysis,then the error functional of asymptotic expansion is obtained.We construct a series to approach the singular point.An extrapolation algorithm is presented and the convergence rate of extrapolation algorithm is proved.At last,some numerical results are presented to confirm the theoretical results and show the efficiency of the algorithms.

SVD-MPE: An SVD-Based Vector Extrapolation Method of Polynomial Type

An important problem that arises in different areas of science and engineering is that of computing the limits of sequences of vectors , where , N being very large. Such sequences arise, for example, in the solution of systems of linear or nonlinear equations by fixed-point iterative methods, and are simply the required solutions. In most cases of interest, however, these sequences converge to their limits extremely slowly. One practical way to make the sequences converge more quickly is to apply to them vector extrapolation methods. Two types of methods exist in the literature: polynomial type methods and epsilon algorithms. In most applications, the polynomial type methods have proved to be superior convergence accelerators. Three polynomial type methods are known, and these are the minimal polynomial extrapolation (MPE), the reduced rank extrapolation (RRE), and the modified minimal polynomial extrapolation (MMPE). In this work, we develop yet another polynomial type method, which is based on the singular value decomposition, as well as the ideas that lead to MPE. We denote this new method by SVD-MPE. We also design a numerically stable algorithm for its implementation, whose computational cost and storage requirements are minimal. Finally, we illustrate the use of SVD-MPE with numerical examples.

GENERALIZED INVERSE RATIONAL EXTRAPOLATION METHODS FOR MATRIX SEQUENCES

Assume that a convergent matrix sequence{An}:An→A（n→∞）, An,A∈C3×3.We want to form a new matrix sequence {Hn}, derived from {An}, which has also A aslimit and whose convergence is faster than the of {An}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {An} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is

EXTRAPOLATION FOR COLLOCATION METHOD OF THE FIRST KIND VOLTERRA INTEGRAL EQUATIONS

1. Introduction It is known that the following Cauchy problem for a parabolic partial differential equation (where the values at the right boundary, u.(1, t)=v(t) are unknown and sought for) is ill-posed: the solution (v) does not depend continuously on the data (g). In order to treat the ill-posedness and develop the numerical method, one reformulates the problem as a Volterra integral equation of the first kind wish a convolution type kernel (see Sneddon [1], Carslaw and Jaeger [2])

Submarine Magnetic Field Extrapolation Based on Boundary Element Method

In order to master the magnetic field distribution of submarines in the air completely and exactly and study the magnetic stealthy performance of submarine,a mathematic model of submarine magnetic field extrapolation is built based on the boundary element method(BEM).An experiment is designed to measure three components of magnetic field on the envelope surface surrounding a model submarine.The data in different heights above the model submarine are obtained by use of tri-axial magnetometers.The results show that this extrapolation model has good stabilities and high accuracies compared the measured data with the extrapolated data.Moreover,the model can reflect the submarine magnetic field distribution in the air exactly,and is valuable in practical engineering.

基于Extrapolation Tikhonov正则化算法的重力数据三维约束反演

通过研究重力数据三维反演解的病态性,利用基于拉格朗日插值方法的Extrapolation Tikhonov正则化方法来解决反演中解的不唯一性和不稳定性问题,该方法最大限度的减少了因正则化参数的引入而在反演结果中介入的误差,同时详细讨论了基于三种选择原则的正则化双参数的具体选择方法,模型试算结果表明,与原Tikhonov方法相比,该方法提高了反演的拟合精度.其次,为了消除核函数随深度增加而快速衰减对反演结果的影响,本文改进了前人的重力数据三维反演深度加权函数,改进后的加权函数与原函数相比能更好的识别异常体底部密度分布特征,对于埋深较深的异常体具有较好的识别效果,更好的解决了由近地面趋肤效应作用引起的密度分布不均的问题.同时,利用上下限约束函数限制每一个立方体的密度差范围,并应用于多组人工合成模型.结果表明:该反演方法能准确地获得正演模型的预设参数范围和位置.

Extrapolated Tikhonov method and inversion of 3D density images of gravity data

Tikhonov regularization（TR） method has played a very important role in the gravity data and magnetic data process. In this paper, the Tikhonov regularization method with respect to the inversion of gravity data is discussed. and the extrapolated TR method（EXTR） is introduced to improve the fitting error. Furthermore, the effect of the parameters in the EXTR method on the fitting error, number of iterations, and inversion results are discussed in details. The computation results using a synthetic model with the same and different densities indicated that. compared with the TR method, the EXTR method not only achieves the a priori fitting error level set by the interpreter but also increases the fitting precision, although it increases the computation time and number of iterations. And the EXTR inversion results are more compact than the TR inversion results, which are more divergent. The range of the inversion data is closer to the default range of the model parameters, and the model features and default model density distribution agree well.

Ballistic Trajectory Extrapolation and Correction of Firing Precision for Multiple Launch Rocket System

The research on multiple launch rocket system(MLRS)is now even more demanding in terms of reducing the time for dynamic calculations and improving the firing accuracy,keeping the cost as low as possible.This study employs multibody system transfer matrix method(MSTMM),to model MLRS.The use of this method provides effective and fast calculations of dynamic characteristics,initial disturbance and firing accuracy.Further,a new method of rapid extrapolation of ballistic trajectory of MLRS is proposed by using the position information of radar tests.That extrapolation point is then simulated and compared with the actual results,which demonstrates a good agreement.The closed?loop fire correction method is used to improve the firing accuracy of MLRS at low cost.

High accuracy eigensolution and its extrapolation for potential equations

From the potential theorem, the fundamental boundary eigenproblems can be converted into boundary integral equations （BIEs） with the logarithmic singularity. In this paper, mechanical quadrature methods （MQMs） are presented to obtain the eigensolutions that are used to solve Laplace＇s equations. The MQMs possess high accuracy and low computation complexity. The convergence and the stability are proved based on Anselone＇s collective and asymptotical compact theory. An asymptotic expansion with odd powers of the errors is presented. By the h3-Richardson extrapolation algorithm （EA）, the accuracy order of the approximation can be greatly improved, and an a posteriori error estimate can be obtained as the self-adaptive algorithms. The efficiency of the algorithm is illustrated by examples.

A New Proposal for Vertical Extrapolation of Offshore Wind Speed and an Assessment of Offshore Wind Energy Potential for the Hibikinada Area, Kitakyushu, Japan

The author’s research group has been conducting research on applications of various meteorological Grid Point Value (GPV) data offered by the Japan Meteorological Agency (JMA) to the field of wind power generation. In particular, the group’s research has been focusing on the following areas: 1) the use of GPV data from the JMA Meso-Scale Model (MSM-S;horizontal resolution: 5 km) and the JMA Local Forecast Model (LFM-S;horizontal resolution: 2 km), and 2) examinations of the prediction accuracy of local wind assessment with the use of these data. In both the MSM-S and the LFM-S, grid points are fixed at 10 m above the sea (ground) surface. The purpose of the present study is to establish a method in which the values of the MSM-S and LFM-S wind speed data from the 10 m height are used as the reference wind speed and are, using a power law, vertically extrapolated to 80 to 90 m heights, typical hub-heights of offshore wind turbines. For this purpose, the present study examined time-averaged vertical profiles of wind speed over the ocean based on the MSM-S data and in-situ data in the Hibikinada area, Kitakyushu City, Fukuoka Prefecture, Japan. As a result, it was revealed that a strong wind shear existed close to the sea surface, between the 10 and 30 m heights. In order to address the above-mentioned wind shear, a two-step vertical extrapolation method was proposed in the present study. In this method, two values of N, specifically for low and high altitudes (below and above approximately 30 m, respectively), were calculated and used. The data were created for the five years between 2012 and 2016. Similarly to previous analyses, the analysis of the created data set indicated that the potential of offshore wind power generation in the Hibikinada area, Kitakyushu City is quite high.

Extrapolation of Explicit DIMSIMs of High Order to Solve the Ordinary Differential Equations

The purpose of this research is to investigate the effciency of explicit diagonally implicit multi-stage integration methods with extrapolation. The author gave detailed explanation of explicit diagonally implicit multi-stage integration method and compared the base method with a technique known as extrapolation to improve the effciency. Extrapolation for symmetric Runge-Kutta method is proven to improve the accuracy since with extrapolation the solutions exhibit asymptotic error expansion, however for General linear methods, it is not known whether extrapolation can improve the effciency or not. Therefore this research focuses on the numerical experimental results of the explicit diagonally implicit multistage integration with and without extrapolation for solving some ordinary differential equations. The numerical results showed that the base method with extrapolation is more effcient than the method without extrapolation.

Extrapolation of GLMs with IRKS Property to Solve the Ordinary Differential Equations

The extrapolation technique has been proved to be very powerful in improving the performance of the approximate methods by large time whether engineering or scientific problems that are handled on computers. In this paper, we investigate the efficiency of extrapolation of explicit general linear methods with Inherent Runge-Kutta stability in solving the non-stiff problems. The numerical experiments are shown for Van der Pol and Brusselator test problems to determine the efficiency of the explicit general linear methods with extrapolation technique. The numerical results showed that method with extrapolation is efficient than method without extrapolation.

LeaderRank的外推加速方法

复杂网络中的节点排序在网络结构和传播动力学等研究中占据重要地位.LeaderRank作为一种重要的节点排序算法,已得到了广泛应用.在幂法计算LeaderRank的基础上,提出3种计算LeaderRank的外推方法,分别为Aitken外推法、幂外推法和改进幂外推法.为了对比各方法的优劣,在4个真实网络上进行数值实验,结果表明:Aitken外推法的计算速度优于幂外推法,而精度略差于幂外推法;改进幂外推法则在计算速度和精度上均有优良表现.

山洪灾害雨量预警指标分析方法评述与展望

山洪灾害预警指标是山洪灾害预报预警的核心,我国现阶段主要采用经验法和水位流量反推法确定雨量预警指标,并逐步推广应用复合预警指标法和动态临界雨量法。在系统阐述国内外常用雨量预警指标分析方法及其特点基础上,针对山洪灾害预警指标分析中需考虑的降雨时空分布变化、高含砂水流、泥石流及其他不确定因素影响问题,提出今后雨量预警指标研究方向。

光伏电站理论发电功率的优化计算模型与方法

光伏电站理论发电功率计算结果的准确性直接影响弃光电量的统计,对电网调度及光伏发展规划影响重大。理论发电功率的传统计算方法有样板逆变器法和气象数据外推法,当样板逆变器的出力受到限制时,样板逆变器法计算结果不准确,而气象数据外推法参数众多且难以确定。针对上述问题,提出了一种光伏电站理论发电功率优化计算方法。首先,介绍了样板逆变器法和气象数据外推法的计算原理,并分析了两种方法的特点和不足。然后,基于光伏电站历史出力及气象信息,提出了改进样板逆变器法和改进气象数据外推法。在实际应用中,当弃光未发生或者在弃光初始阶段采用计算精度更高的改进样板逆变器法开展计算,当样板逆变器出力受到限制时,切换至改进气象数据外推法进行求解。最后,对国内某光伏电站在不同气象条件下开展仿真计算,验证了所提方法的合理性和有效性。