2005年工作年报



一、机构设置和研究人员
二、科学研究方向、项目和经费
三、科学研究成果
四、学术活动
五、学科建设和人才培养
六、工作环境及实验室建设
七、2005年论文摘要

一、机构设置和研究人员
1.根据《上海市高校计算科学E—研究院建设总体规划书》和《上海市高校计算科学E—研究院管理章程》等文件,制订和执行2005年度工作计划。
2.郭本瑜教授为首席研究员,并聘请下列专家为特聘研究员
  • 张伟江 上海交通大学教授
  • 程晋 复旦大学教授
  • 黄建国 上海交通大学教授
  • 丛玉豪 上海师范大学教授
  • 岳荣先 上海师范大学教授
  • 王元明 华东师范大学教授
  • 徐承龙 同济大学教授
  • 田红炯 上海师范大学教授
  • 王中庆 上海师范大学副教授
3.由下列专家组成学术委员会。
  • 主任:石钟慈 中国科学院院士
  • 委员:林群 中国科学院院士
  • 姜礼尚 同济大学教授
  • 郭本瑜 上海师范大学教授
  • 张伟江 上海交通大学教授
  • 吴宗敏 复旦大学教授
  • 马和平 上海大学教授
  • 香港城市大学王世全教授为研究院顾问。
4.田红炯教授兼任业务秘书,王维敏同志任行政秘书。


二、科学研究方向、项目和经费
1.根据研究院科学研究方向,制订并资助本年度研究课题,承担国家和上海市其它科研项目,积极申请新的科研项目。
2.目前的主要研究方向:
  • 数学物理问题的高精度算法
  • 动力系统的数值研究
  • 弹性组合结构的数值方法
  • 金融随机模型的数值方法
  • 伪蒙特卡罗方法
  • 反问题的数值方法
3.本年度资助下列研究课题,共30.5万。
  • 郭本瑜数学物理问题的高精度算法
  • 程晋数学物理反问题的理论和数值方法
  • 黄建国组合弹性结构问题的有限元方法
  • 岳荣先随机伪蒙特卡罗方法的理论与应用
  • 田红炯滞时微分动力系统的数值方法
  • 丛玉豪常微分数值方法在求解时滞方程及Hamilton系统中的应用
  • 徐承龙金融衍生物的偏微分方程定价及计算
  • 王元明非线性初(边)值问题的高精度有限差分方法
  • 王中庆奇异问题和无界区域问题的谱方法
4.特聘研究员承担了14项国家和上海市科研项目,本年度到达的研究总经费112万元。
A.国家科研项目5个,本年度到达经费77.6万元。
  • 程晋     国家自然科学基金重点项目,数学物理方程反问题及其应用。
  • 郭本瑜   国家自然科学基金项目,奇异问题及非矩形和无界区域问题的谱方法。
  • 岳荣先   国家自然科学基金,多因变量回归模型的稳健设计。
  • 黄建国   国家自然科学基金,组合弹性结构动力学问题数值解研究。
  • 徐承龙   国家自然科学基金,粘性解及其在金融中的应用。
B.上海市及教育部科研项目9个,本年度到达经费34.4万元。
  • 郭本瑜   上海市科委重点项目,若干数学物理复杂问题的计算方法。
  • 郭本瑜   国家教育部博士点基金,奇异问题和无界区域问题的谱方法及其应用。
  • 程晋     上海市教委曙光计划基金,数学物理反问题。
  • 田红炯   上海市科委启明星计划基金,滞时微分动力系统的数值分析。
  • 田红炯   上海市优秀青年教师后备人选研究基金,中立型微分系统的数值分析。
  • 王中庆   上海市教委科研基金,奇异和无界区域问题的高精度算法。
  • 王元明   国家回国留学生科研基金,非线性反应扩散方程的高精度有限差分方法及其数值分析。
  • 丛玉豪 上海市教委科研基金,非自治无穷维Hamilton系统的多辛几何算法。
  • 岳荣先 上海市教委科研基金,随机化伪Monte Carlo积分法的易处理性研究。
5.最近申请并获准主持或参加3个国家和上海市科研项目,总经费36万元。这些项目将从2006年开始执行。
  • 程晋     教育部新世纪人才计划项目。
  • 程晋     国家重大基础研究项目《针刺效应与经络功能的科学基础》,数学模型。
  • 王元明   国家自然科学基金,非线性椭圆边值问题的高精度紧有限差分方法。

三、科学研究成果
本年度在奇异和无界区域问题、动力系统、组合弹性力学,及反问题的数值解法等方面取得了一批研究成果,出版学术专著1部,在国内外重要学术刊物上发表了21篇论文,其中某些结果是原创性的。
1.数学物理问题的高精度算法(郭本瑜,王中庆,徐承龙)
  • 建立了非一致权函数Sobolev空间中的高阶Jacobi正交逼近理论,并由此提出四阶奇异微分方程的谱方法。计算结果显示了该方法的高精度。
  • 引入了一类新的广义Laguerre多项式系,建立了有关混合正交逼近理论,并由此提出三维问题的新谱方法。数值实验表明了它的优越性。
  • 应用广义Fourier-Laguerre 混合正交逼近方法计算外部问题,首次证明 
  • 外部问题谱方法的收敛性。
  • 构建了无限长条区域上的Laguerre-Hermite混合插值理论及有关拟谱方法,并应用于热传导问题。
有关论文:
[1]Ben-yu Guo, Zhong-qing Wang, Zheng-su Wan and Delin Chu, Second order Jacobi approximation with applications to fourth order differential equations, Appl. Numer. Math., 55(2005),480-502.
[2]Guo Ben-yu and Zhang Xiao-yong, A new generalized Laguerre spectral approximation and its applications, J. of Comp. and Appl. Math,. 181(2005), 342-363.
[3]Ben-yu Guo, Jie Shen and Cheng-long Xu, Generalized Laguerre approximation and  its applicatios to exterior problems,  J. of Comp Math., 23(2005), 113-130.
[4]Wang Tian-jun and Guo Ben-yu, Mixed Leguerre-Hermite pseudospectral method for heat transfer in infinite plate, J. of Comp. Math., 23(2005), 587-602.
2.动力系统的数值方法(丛玉豪,田红炯)
  • 基于线性滞时微分方程建立了线性θ—方法的数值耗散性,它有助于对滞时动力系统及其数值方法的研究。
  • 分析了计算广义时滞微分方程系统的θ方法的渐近稳定性,证明了其GP-稳定当且仅当1/2≤θ≤1,单支θ-方法是GP-稳定当且仅当θ=1。
  • 研究了Runge-Kutta 方法求解广义时滞微分方程系统的GPL-稳定性,证明了隐式Runge-Kutta方法是GPL-稳定的,当且仅当它是L-稳定的。
有关学术专著和论文:
[1]Kuang Jiaoxun and Cong Yuhao, Stability of Numerical Methods for Delay Differential Delay , Science Press,Beijing, 2005.
[2]Cong Yuhao, Zhang Yuanying and Xiang Jiaxiang, The GPL—stability of Runge—Kutta methods for generalized delay differential systems, J. of syst. Simul., 17 (2005), 587-589, 594.
[3]L. Fan, Y. Zhang, J. Xiang, and H. Tian, Numerical dissipativity of two-stage  -method for delay differential equations, J. Syst. Simu., 17(2005), 599-600, 634.
3.组合弹性结构问题的有限元方法(黄建国)
  • 给出一个求解由函数近似均值重构函数的正则化方法,证明了解的存在唯一性,建立了相应的误差分析理论,并通过系列数值实验提供了正则化参数选取的实用策略。
  • 通过变分原理,获得由任意多个体、板、梁耦刚接而成的组合弹性结构问题数学模型;获得了一个广义Korn不等式,从而证明模型解的存在唯一性;在对解作合理的正则化假设下得到了结构的所有平衡方程。
  • 提出一个求解一般组合弹性结构问题的有限元方法。对体件的位移,板件的纵向位移和杆件的纵向位移用线性协调元离散;对杆件的纵向转角用二次协调元离散;对板件的横向位移和杆件的横向位移分别用Morley元和三次Hermite元离散。在相应的非协调元空间上建立了广义Korn不等式,进而证得有限元方法的唯一可解性,并导出最优误差估计。
  • 给出了一个广义Kantorovich不等式的最有化证明方法,并推广至矩阵情形。
有关论文:
[1]J. Huang and Y. Chen, A regularization method for the function reconstruction from approximate average fluxes, Inverse Problems, 21(2005), 1667-1684.
[2]J. Huang, Z. Shi and Y. Xu, Some studies on mathematical models for general elastic multi-structures, Science in China Ser. A, 48:7(2005), 986-1007.
[3]J. Huang, Z. Shi and Y. Xu, Finite element analysis for general elastic multi-structures (Chinese), Science in China Ser. A, 35:10(2005), 1100-1119.
[4]J. Huang and J. Zhou,  A direct proof and a generalization for a Kantorovich type inequality, Linear Algebra and its  Applications, 297(2005), 185-192.
4.金融衍生物的偏微分方程定价及计算(徐承龙)
  • 对具有跳扩散的美式期权的二叉树方法,证明了算法的收敛性,并得到了最佳实施边界的起始点位置及单调性质。
  • 对具有回望性质的欧式期权,在偏微分方程的模型下得到了带一般收益函数的解的表达式。此结果有助于研究具有回望性质的美式期权。
有关论文:
[1]Qian Xiao-song, Xu Cheng-long, Jiang Li-shang and Bian Bao-jun, Convergence of Binomial tree method for American options in a jump-diffusion model,  SIAM J. of Numer. Comp., 42(2005), 1899 - 1913.
[2]Chenglong Xu and Yue Kuen Kwok, Integral price formulas for lookback options,  Journal of Appl. Math., 2005:2, 117-125.
5.非线性初(边)值问题的高精度有限差分方法(王元明)
  • 对一类线性四阶边值问题解的存在唯一性给出了定性刻划,为进一步构造该问题高精度数值方法提供了理论基础。
  • 对一类半线性椭圆边值问题的有限差分解发展了一种加速单调迭代算法,该算法产生的迭代序列不仅具有单调性而且具有二次收敛率。由于不需要非线性函数的单调性假设,该算法的适用性优于牛顿法。
  • 对一类非线性高阶Lidstone椭圆边值问题建立了解的存在唯一性定理,以及单调迭代算法。
有关论文:
[1]Yuan-Ming Wang, On fourth-order elliptic boundary value problems with nonmonotone nonlinear functions, J. Math. Anal. Appl., 307(2005), 1--11.
[2]Yuan-Ming Wang, On accelerated monotone iterations for numerical solutions of semilinear elliptic boundary value problems, Applied Mathematics Letters, 18(2005), 749—755.
[3]Yuan-Ming Wang, Higher-order Lidstone Boundary Value Problems for Elliptic Partial Differential Equations, J. Math. Anal. Appl.,  308(2005), 314—333.
[4]Yuan-Ming Wang, On 2nth-order Lidstone boundary value problems, J. Math. Anal. Appl. , 312 (2005), 383-400.
6.随机伪蒙特卡罗方法的理论与应用(岳荣先)
  • 对于加权的再生核Hilbert空间的情形,通过b-进制Haar小波基函数引进权重系数,它表示随着函数自变量维数的增加而其显著性依次减小。同时证出了积分法具有O(n-1)与O(n-3/2)收敛速度的函数空间的加权系数所应满足的充分条件。
  • 对于加权的Banach空间的情形,假定被积函数的一阶混合偏导数在Lp模意义下有界,而权重系数通过lp模引进,把加权再生核Hilbert空间中的结果推广到加权Banach空间的情形。
有关论文:
[1]Rong-Xian Yue, Fred J. Hickernell, Strong tractability of integration using scrambled Niederreiter points, Mathematics of Computation, 74(2005), 1871-1893.
[2]Yue Rongxian, Asymptotic Bayesian design nonparametric mutiresponse prediction. 应用概率统计, 21(2005),113-120.
7.数学物理反问题的理论和数值方法(程晋)
  • 发展了本人提出的Cine unique contiuation概念,应用它讨论具有局部数据的反问题,还证明利用解的局部数据可以决定未知函数的局部信息。
  • 提出了一种计算逆散射问题的直接方法,它克服把原问题转化为优化问题所带来的缺点,即需要不断求解正问题,即使我们只需要解的部分信息,我们也不得不将解的所有信息都解出来。
  • 研究了一种名为探测方法(Probe method)的数学理论和数值实现,给出了一种同时重构边界和阻尼系数的方法。
有关论文:
[1]J. Cheng, L. Peng and M. Yamamoto, The conditional stability in line unique continuation for a wave equation and an inverse wave source problem, Inverse Problems, 21 (2005), 1993-2007.
[2] J. Cheng, J. J. Liu and G. Nakamura,The numerical realization of the probe method for the inverse scattering problem from the near filed data. Inverse Problems, 21(2005), 839-855.
[3]J. Cheng, C. L. Lin and G. Nakamura,Unique continuation along curves and hypersrufaces for second order anisotropic hyperbolic systems with real analytic coefficients. Proc. Amer. Math. Soc., 133(2005), 2359-2367.


四、学术活动
遵循研究院管理章程进行日常学术活动,并举办或合办了一些国内或国际学术会议。
1.日常学术活动
每月召开全体特聘研究员工作会议,相互交流科学研究工作并部署下一步研究工作。
每月举办一次面向全市的学术报告会,由特聘研究员或院外专家介绍科学计算的新进展。
邀请30名国内外专家来研究院讲学或合作研究。
研究院8位成员参加了国际学术会议,共15人次,并作邀请报告或报告。多名研究员到国外或境外讲学或短期合作研究。
2.举办或合办国内、外学术会议
2004年1月,举办数值代数研讨会,参加者约60人。
2004年6月,与上海交通大学合办第四届科学计算及其应用国际会议,参加者约150人。
3.拟办的学术会议
2006年夏季,举办动力系统及其数值模拟国际学术会议。
2006年秋季,举办第二次上海市科学与工程计算研讨会。


五、学科建设和人才培养
根据研究院的宗旨,促进上海市有关学校的《计算科学》学科建设,加速培养计算科学专业的学术带头人和其它专业人才。
1.上海师范大学《科学计算及仿真技术》学科被评为上海市重点建设学科。
2.郭本瑜教授被聘为国家重大基础研究项目《高性能计算研究》专家委员会委员。
3.特聘研究员岳荣先担任中国现场统计研究会副理事长。
4.特聘研究员田红炯晋升为正教授。特聘研究员徐承龙被评为计算数学学科博士生指导教师。
5.特聘研究员王中庆获得2005年上海市优秀博士论文奖(2002年毕业)。
6.研究院成员共指导了14名博士生(其中毕业4名),和32名硕士生(其中毕业10名)。黄建国教授指导博士后1名。


六、工作环境及实验室建设
按计划完成了工作环境及实验室建设。
1.配备了视频系统。
2.筹划SGI-300高性能工作站扩能工作。


七、2005年论文摘要
The numerical realization of the probe method for the inverse scattering problems from the near-field data
J. Cheng, J. J. Liu and G. Nakamura
Inverse Problems 21(2005), 1993-2007.
Abstract
In this paper, we present some results on the numerical realization of the probe method for the inverse scattering problem of determining an obstacle with impedance boundary condition from the near-field data. The keys are how to construct the Runge approximate function for the fundamental solutions and compute the indicator function for the boundary of an obstacle. We test the performance of the probe method for a 2D obstacle by taking the simulated Dirichlet-to-Neumann map as inversion input data.

The conditional stability in line unique continuation for a wave equation and an inverse wave source problem
J. Cheng, L. Peng and M. Yamamoto
Inter. J. of bifurration and Chaos, 14(2004), 1839-1845.
Abstract
In this paper, we prove a conditional stability estimate of the logarithmic type for a wave equation on a line in Rn, 2 _ n _ 3 by combining the Fourier– Bros–Iagolnitzer transformation. Then we apply it to an inverse wave source problem of determining a spatially varying source term on its extended line by observations of a segment and establish the conditional stability.

Unique continuation along curves and hypersurfaces for second order anisotropic hyperbolic systems with real analytic coefficients
J. Cheng, C. L. Lin and G. Nakamura
Proc. Amer. Math. Soc., 133(2004), 2359-2367.
Abstract
In this paper we prove the following kind of unique continuation property. That is, the zero on each geodesic of the solution in a real analytic hypersurface for second order anisotropic hyperbolic systems with real analytic coe.cients can be continued along this curve.

The GPL-stability of Runge-Kutta methods for generalized delay differential system
Y. H. Cong, Y. Y. Zhang and J. X. Xiang
J. syst. simu., 17(2005), 587-589, 594.
Abstract
It is discussed the asymptotic stability analysis of the IRK-method for the numerical solution of generalized delay differential equations. The GPL-stability behavior of IRK-method is analyzed for the solutions of the system of linear test equations. It is shown that the IRK-method is GPL-stable if and only if it is L-stable.

Numerical dissipativity of two-stage  -method for delay differential equations
L. Q. Fan, Y. Y. Zhang, J. X. Xiang and H. J. Tian
J. syst. Simu., 17(2005), 599-600, 634.
Abstract
It is focused on numerical dissipativity of two-stage  -methods for delay differential equations with a constant lag. It is proved that the two-stage  -method is dissipative if and only if  . One numerical experiment is given to illustrate our result.

Second order Jacobi approximation with applications to fourth-order differential equations
B. Y. Guo, Z. Q. Wang, Z. S. Wan and D. L. Chu
Applied Numerical Mathematics, 55(2005), 480-502.
Abstract
Second order  Jacobi approximation in  non-uniformly weighted obolev space is investigated. Some approximation results on arious orthogonal projections are established, which serve as the athematical foundation of Jacobi spectral methods for ifferential equations of fourth-order. Jacobi spectral schemes re provided  for several model problems. The convergence is roved. Numerical results agree well with  theoretical analysis and show the efficiency of this new approach.

A new generalized Laguerre spectral approximation and its applications
B. Y. Guo and X. Y. Zhang
Journal of Computational and Applied Mathematics, 181(2005), 342-363.
Abstract
A new family of generalized Laguerre polynomials is introduced. arious  orthogonal projections are investigated. Some approximation results are established.  As an example of their important pplications, the mixed spherical harmonic-generalized Laguerre approximation  is developed. A ixed spectral scheme is proposed for a three-dimensional model roblem. Its convergence is proved. Numerical esults demonstrate the high accuracy  of this new spectral method.

Generalized Laguerre approximation and its applications to exterior problems
B. Y. Guo, J. Shen and C. L. Xu
Journal of computational Mathematics, 23(2005), 113-130.
Abstract
Approximations using the generalized Laguerre polynomials are nvestigated in this paper. Error estimates for various orthogonal rojections are established. These estimates generalize and mprove previously published results on the Laguerre pproximations. As an example of applications, a mixed aguerre-Fourier spectral method for the Helmholtz equation in an xterior domain is analyzed and implemented. The proposed method njoys  optimal error estimates, and with suitable basis unctions, leads to a sparse and symmetric linear system.

A regularization method for the function reconstruction from approximation average fluxes
J. G. Huang and Y. Chen
Inverse Problems, 21(2005), 1667-1684.
Abstract
A regularization method is proposed for the function reconstruction from pproximate average fluxes. Such problems often occur in environmental science and mathematical statistics. The unique solvability of the method is proved and a number of conditions are given to characterize the solution. The error estimates are established after the introduction of some interpolation operators. A series of numerical examples are provided to illustrate the effectiveness and computational performance of the method. Some ideas for the choice of the regularization parameter are also suggested by the computational experience.

Some studies on mathematical models for general elastic multi-structures
J. G. Huang, Z. C. Shi and Y. F. Xu
Science in China ser A, 48(2005), 986-1007.
Abstract
The aim of this paper is to study the static problem about a general elastic multi-structure composed of an arbitrary number of elastic bodies, plates and rods. The mathematical model is derived by the variational principle and the principle of virtual work in a vector way. The unique solvability of the resulting problem is proved by the Lax-Milgram lemma after the presentation of a generalized Korn's inequality on general elastic multi-structures. The equilibrium equations are obtained rigorously by only assuming some reasonable regularity of the solution. An important identity is also given which is essential in the finite element analysis for the problem.

一般组合弹性结构的有限元分析
J. G. Huang, Z. C. Shi and Y. F. Xu
中国科学,A辑 35(2005), 1100-1119.
Abstract
A finite element method is introduced to solve the general elastic multi-structure problem, in which the displacements on bodies, the longitudinal displacements on plates and the longitudinal displacements on beams are discretized using conforming linear elements, the rotational angles on beams are discretized using conforming elements of second order, the transverse displacements on plates and beams are discretized by the Morley elements and the Hermite elements of third order, respectively. The generalized Korn's inequality is established on related nonconforming element spaces, which implies the unique solvability of the finite element method. Finally, the optimal error estimates in the energy norm are derived for the method.
A direct proof and a generalization for a Kantorovich type inequality
J. G. Huang and J. Y. Zhou
Algebra and its Applications, 397(2005), 185-192.
Abstract
A direct proof for a Kantorovich type inequality due to Bauer and Householder is presented. A generalization of the inequality is also established by the theory of compound matrices.

Convergence of the binomial tree method for American options in a jump-diffusion model
X. S. Qian, C. L. Xu, L. S. Jiang and B. J. Bian
SIAM J. of Numer. Comp., 42(2005), 1899-1913.
Abstract
A direct proof for a Kantorovich type inequality due to Bauer and Householder is presented. A generalization of the inequality is also established by the theory of compound matrices.

Mixed Legendre-Hermite pseudospectral method for heat transfer in an infinite plane
T. J. Wang and B. Y. Guo
Journal of Computational Mathematics, 23(2005), 587-602.
Abstract
A new mixed Legendre-Hermite interpolation is introduced.  Some approximation results are established. Mixed Legendre-Hermite pseudospectral method is proposed  for non-isotropic heat transfer in an infinite plate. Its convergence is proved. Numerical results show the efficiency of this  approach.

On fourth-order elliptic boundary value problems with nonmonotone nonlinear function
Y. M. Wang
J. Math. Anal., Appl., 307(2005), 1-11.
Abstract
This paper is concerned with the fourth-order elliptic boundary value problems with nonmonotone nonlinear function.  The existence and uniqueness of a solution  is proven by the method of upper and lower solutions. A monotone iteration is developed so that the iteration sequence converges monotonically to a maximal solution or a minimal solution, depending on whether the initial iteration is an upper solution or a lower solution.

Higher-order Lidstone boundary value problems for elliptic partial differential equations
Y. M. Wang
J. Math. Anal. Appl., 308(2005), 314-353
Abstract
The aim of this paper is to show the existence and uniqueness of a solution for a class of 2nth-order  elliptic Lidstone boundary value problems  where the nonlinear functions depend on the higher order derivatives. Sufficient conditions are given for the existence and uniqueness of a solution. It is also shown that there exist two sequences which converge monotonically from above and below, respectively, to the unique solution.  The approach to the problem is by the method of upper and lower solutions together with monotone iterative technique for nonquasimonotone functions. All the results are directly applicable to 2nth-order two-point Lidstone boundary value problems.

On 2nth-order Lidstone boundary value problems
Y. M. Wang
J. Math. Anal. Appl., 312(2005), 383-400.
Abstract
This paper is concerned with the solutions of a class of 2nth-order Lidstone boundary value problems. Sufficient conditions for the existence and uniqueness of a solution are given. A monotone iteration is developed so that the iteration sequence converges monotonically to a maximal or a minimal solution. The approach to the problem is by the method of upper and lower solutions with a new maximum principle.

On accelerated monotone iterations for numerical solutions of semilinear elliptic boundary value problems
Y. M. Wang
Appl. Math. Letters, 18(2005), 749-755.
Abstract
This paper is concerned with the computational algorithms for finite difference solutions of a class of semilinear elliptic boundary value problems. An accelerated monotone iterative scheme is presented by using the method of upper and lower solutions. The rate of convergence of the iterations is estimated by infinity norm, and the rate of convergence is quadratic for a larger class of nonlinear functions, including monotone nonincreasing functions.  An application is given to a logistic model problem in ecology.

Integral price formulas for lookback options
C.L. Xu and Y. K. Kwok
J. of Appl. Math., 2005:2(2005), 117-125.
Abstract
We derive an integral representation of the price formulas for European options whose terminal payoff involves path-dependent lookback variable. The intricacies in the derivation procedures using the partial differential equation techniques stem from the degenerate nature of the pricing models, where the lookback state variables appear only in the auxiliary conditions but not in the governing differential equations.We also derive a parity relation between the price functions of the floating strike and fixed strike lookback options.

Strong tractability of integration using scrambled Niederreiter points
R. X. Yue and F. J. Hickernell
Mathematics of computation, 74(2005), 1871-189.
Abstract
We study the randomized worst-case error and randomized error of scrambled quasi-Monte Carlo (QMC) quadrature as proposed by Owen (1995). The function spaces considered in this article are the weighted Hilbert spaces generated by Haar-like wavelets and the weighted Sobolev-Hilbert spaces. Conditions are found under which multivariate integration is strongly tractable in the randomized worst-case setting and randomized setting, respectively. The -exponents of strong tractability are found for the scrambled Niederreiter nets and sequences. The sufficient conditions for strong tractability for Sobolev spaces are more lenient for scrambled QMC quadratures than those for deterministic QMC net quadratures (Wang, 2003).
Asymptotic Bayesian design nonparametric multiresponse prediction
R. X. Yue
应用概率统计,21(2005), 113-120.
Abstract
This paper deals with Bayesian design in the unit cube for multiresponse prediction with infinite-dimensional random functions as priors. In order to make optimization more tractable, we adopt the asymptotics used in Mitchell et al. (1994). It is shown that the uniform continuous design on the unit cube is optimum under the asymptotic Bayes criterion for a certain prior specification. It follows that the uniform design proposed by Fang and Wang (1994) performs very well for the multiresponse prediction.

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发布日期: 2005/12/31
浏览次数: 1290

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