多电极成像测井反演问题的数学模型和数学方法

多电极成像测井是一种新的电阻率测井技术,这一测井技术的电极系中包含有多个测量电极,可提供较多的测量信息,从而有助于用较高的分辨率确定地层电阻率参数。本文对这个问题建立了数学模型,且运用非线性优化等数学方法对多电极成像测井反演问题提出了数值求解方法。并利用一些数值结果证实了这些算法的有效性。     

核磁共振弛豫信号的多指数反演

从第一类积分方程的反演求解入手,推导出适合于岩石核磁共振弛豫时间多指数反演的两种算法：奇异值分解（singular value decomposition）方法和变换反演算法.对算法的具体实现过程进行了详细的论述,从理论和实例处理两方面分析讨论了两种算法的优缺点.从解的自由度的角度,讨论解的分辨率及最优反演模型的选取原则：SVD算法适合于信噪比较高的数据反演,变换反演算法适应于较低信噪比的数据反演.在进行岩石核磁共振信号的多指数反演处理时,应优先选用变换反演算法,只有当原始数据的信噪比SNR≥80时,可选用SVD反演算法.为保证T₂反演结果的真实性,T₂布点数应在30～50个之间.[KG*2]研究内容对核磁共振岩心分析和核磁共振测井工作具有重要参考价值.     

Abel变换数值反演的积分算子方法

本文研究了Abel变换的数值反演问题.利用Abel变换的理论反演公式与数值求导的积分算子法相结合的方法,对反演公式中奇异积分合理处理,获得Abel变换数值反演的一种算法,并进行了理论分析与数值实验. 结果表明该算法具有计算简单、数值稳定等优点.     

基于MINRES-QLP截断牛顿法的全波形反演

在全波形反演过程中,二阶梯度信息扮演着重要的作用.然而,由于其巨大的计算量和内存需求,限制了其在全波形反演问题中的应用.本文基于MINRES-QLP方法提出了一种高效的截断牛顿全波形反演方法.该全波形反演方法能够充分利用目标泛函的二阶梯度信息,提高反演精度.MINRES-QLP反演方法还能够利用Hessian阵负特征值信息,从而提高算法的重构分辨率和计算效率.针对Hessian阵计算难题,本文给出了一种矩阵向量相乘的快速算法.基于二维2004 BP模型,Sigsbee模型,验证了MINRES-QLP截断牛顿反演方法的有效性.数值结果表明MINRES-QLP截断牛顿法能充分利用二阶梯度信息和Hessian阵负特征值信息,从而加速算法收敛速度和提高成像精度.     

生物斑图中Gray-Scott模型的数值求解及参数反演

生物斑图中反应扩散模型数值解及其参数反演的研究是非常有趣和重要的.主要以生物斑图中Gray-Scott模型为研究对象,对其正、反问题进行研究,提出了一种新的算法-DE-ME算法,并通过数值算例模拟验证了其在求解Gray-Scott模型参数反演问题中的可行性及有效性.结果表明此混合算法能快速有效地解决此类反应扩散模型参数反演问题.     

用于寻源导热反问题的自适应蚁群算法研究

建立以蚁群算法(ant colony optimization,ACO)为基础的二维稳态导热反问题的求解模型.模型根据边界测点的测量信息与计算所得到的测点温度进行比较,将导热反问题转化为一个优化问题.对蚁群算法进行改进,利用不同路径构造方法的自适应蚁群算法对热源强度、热源位置进行反演,得到较为精确的反演结果.结果表明,所采用的蚁群算法和针对不同反演参数的路径构造方法具有较强的稳定性,能够较好反演热源强度及热源位置.     

涡流检测中识别缺陷形状的一种新方法

涡流检测反演技术是一种非常重要的反演缺陷形状尺寸的无损检测方法.运用Dirichlet边界条件下涡流检测反演的远场区域导数,构造了反演缺陷形状的一种新算法,并且给出了二维及三维的算例,数值反演的结果与实际缺陷吻合得较好.从而说明了:对较小的波数,即使用较少的入射和观测方向的远场测量信息,亦可得到未知缺陷形状的一个合理的重构,算法是可行的、正确的.     

识别含热源瞬态热传导问题的热扩散系数

针对含有热源的瞬态热传导反问题,引入一个变换将含热源热传导问题转换为无热源热传导问题,采用改进布谷鸟算法反演热扩散系数.正问题由边界元法求解.将热扩散系数作为优化变量,以计算温度和测量温度之间的接近程度为目标函数,通过改进布谷鸟算法极小化目标函数来优化估计热扩散系数.比较共轭梯度法、布谷鸟算法和改进布谷鸟算法的反演结果.与共轭梯度法相比,改进布谷鸟算法对迭代初值不敏感;与布谷鸟算法相比,改进布谷鸟算法收敛速度更快.算例讨论了测点数量、鸟巢数量、测量误差对计算结果的影响.增加测点数量,反演结果精度降低;增加鸟巢数量,迭代次数减少;随着测量误差的增大,结果精度降低.数值算例验证了改进布谷鸟算法反演热扩散系数的准确性和有效性.     

云导风的初步探究

针对云导风反演算法进行了深入研究.通过分析卫星云图的灰度特性和纹理特征,提出了基于最大灰度和梯度交叉相关系数的云导风反演方法.依据最大信息熵准则自适应调整窗口大小,根据NCEP数值预报产品指定风矢高度.实验结果表明,方法有效提高了反演的义精度和效率.     

基于快速成像反演算法的地表温度反演可视化技术研究

当前主流的地表温度检测方式是通过遥感反演以及地面实地检测,其中遥感反演虽然检测范围面积较广,但是检测精度较低.利用WATERSHED快速成像反演算法与WATERSHED快速成像反演算法对无锡花海活动进行地表温度的数据分析以及可视化显示,利用算法的优点提高地表温度反演可视化效果.最后利用FAHP模型对快速成像反演算法在地表温度反演可视化实际效果进行评价.结果表明,快速成像反算法可以有效地提高地表温度的反演可视化效果.     

Long-step primal-dual target-following algorithms for linear programming

In this paper we propose a long-step target-following methodology for linear programming. This is a general framework, that enables us to analyze various long-step primal-dual algorithms in the literature in a short and uniform way. Among these are long-step central and weighted path-following methods and algorithms to compute a central point or a weighted center. Moreover, we use it to analyze a method with the property that starting from an initial noncentral point, generates iterates that simultaneously get closer to optimality and closer to centrality.This work is completed with the support of a research grant from SHELL.The first author is supported by the Dutch Organization for Scientific Research (NWO), grant 611-304-028.The fourth author is supported by the Swiss National Foundation for Scientific Research, grant 12-34002.92.     

Trefftz,collocation, and other boundary methods—A comparison

In this article we survey the Trefftz method (TM), the collocation method (CM), and the collocation Trefftz method (CTM). We also review the coupling techniques for the interzonal conditions, which include the indirect Trefftz method, the original Trefftz method, the penalty plus hybrid Trefftz method, and the direct Trefftz method. Other boundary methods are also briefly described. Key issues in these algorithms, including the error analysis, are addressed. New numerical results are reported. Comparisons among TMs and other numerical methods are made. It is concluded that the CTM is the simplest algorithm and provides the most accurate solution with the best numerical stability. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Volume preserving RK methods for linear systems

1. IntroductionIn recent yearss there has been a great interest in constructing numerical integrationschemes for ODEs in such a way that some qualitative geometrical properties of the solutionof the ODEs are exactly preserved. R.th[ll and Feng Kang[2'31 has proposed symplectic algorithms for Hamiltollian systems, and since then st ruct ure s- preserving me t ho ds fordynamical systems have been systematically developed[4--7]. The symplectic algorithms forHamiltonian systems, the volume-pre…     

求解离散不适定问题的正则化GMERR方法

迭代极小残差方法是求解大型线性方程组的常用方法, 通常用残差范数控制迭代过程.但对于不适定问题, 即使残差范数下降, 误差范数未必下降. 对大型离散不适定问题,组合广义最小误差(GMERR)方法和截断奇异值分解(TSVD)正则化方法, 并利用广义交叉校验准则(GCV)确定正则化参数,提出了求解大型不适定问题的正则化GMERR方法.数值结果表明, 正则化GMERR方法优于正则化GMRES方法.     

A note on the biasing of Newton's direction

This note deals with the geometric interpretation of the Levenberg-Marquardt search direction when the augmented Hessian is not positive definite.     

s个几乎相等的素数的k次方和(Ⅰ)

假定pθ‖k,当p=2,2|k时，γ=θ 2；其它情况时，γ=θ 1。而R＝П(p-1)|kp^γ。本文在GRH（广义Riemann假设下），证明了当s=2^k 1,1≤k≤11时，任何足够大的整N≡s(modR)都可以表示为s个几乎相等的素数的k次方程。     

Diagonalized multiplier methods and quasi-Newton methods for constrained optimization

Two approaches to quasi-Newton methods for constrained optimization problems inR ⁿ are presented. These approaches are based on a class of Lagrange multiplier approximation formulas used by the author in his previous work on Newton's method for constrained problems. The first approach is set in the framework of a diagonalized multiplier method. From this point of view, a new update rule for the Lagrange multipliers which depends on the particular quasi-Newton method employed is given. This update rule, in contrast to most other update rules, does not require exact minimization of the intermediate unconstrained problem. In fact, the optimal convergence rate is attained in the extreme case when only one step of a quasi-Newton method is taken on this intermediate problem. The second approach transforms the constrained optimization problem into an unconstrained problem of the same dimension.The author would like to thank J. Moré and M. J. D. Powell for comments related to the material in Section 13. He also thanks J. Nocedal for the computer results in Tables 1–3 and M. Wright for the results in Table 4, which were obtained via one of her general programs. Discussions with M. R. Hestenes and A. Miele regarding their contributions to this area were very helpful. Many individuals, including J. E. Dennis, made useful general comments at various stages of this paper. Finally, the author is particularly thankful to R. Byrd, M. Heath, and R. McCord for reading the paper in detail and suggesting many improvements.This work was supported by the Energy Research and Development Administration, Contract No. E-(40-1)-5046, and was performed in part while the author was visiting the Department of Operations Research, Stanford University, Stanford, California.     

投入产出技术在计划平衡中的理论与应用

在用投入产出技术作计划平衡时，目前一般采用最终产品法、总产品法及国民收入法等．本文从理论上研究了这些方法的可行性问题，并在此基础上提出一个较理想的综合法．最后附有实例并说明综合法的现实意义．     

A comparison of some ODE solvers which require Jacobian evaluations

A variety of third-order ODE solvers which have a minimum configuration (i.e. minimum work per step) have been numerically tested and the results compared. They include implicit and explicit processes, and share the property that a Jacobian matrix must be evaluated at least once during the integration. Some of these processes have not been previously described in the literature.     

On the Convergence of Descent Algorithms

It is proved that any cluster point of a sequence defined by a steepest descent algorithm in a general normed vector space is a critical point. The function is just assumed to be continuously differentiable. The class of algorithms we consider encompasses several choices such as the Cauchy steplength and the Curry steplength.