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向 华
  ==> 个人简介

  姓名:向华

  性别:男

  学历:博士

  专业: 计算数学

  地址:武汉大学数学与统计学院,430071,武汉

  Email: hxiang@whu.edu.cn

 

  教育背景

  ◆ 2003年9月 - 2006年6月, 复旦大学数学科学学院,计算数学专业博士(导师:曹志浩)。

  ◆ 1999年9月 - 2002年6月, 中国科学院力学研究所,流体力学专业硕士(导师:刘青泉)。

  ◆ 1995年9月 - 1999年6月, 哈尔滨工程大学船舶与海洋工程系,船舶工程专业学士。

 

  工作经历

  ◆2016年6月至今,武汉大学数学与统计学院,教授。

  ◆2008年12月– 2016年6月,武汉大学数学与统计学院,副教授。

  ◆2006年7月 – 2008年12月,武汉大学数学与统计学院,讲师。

  ◆2009年1月 – 2009年12月, Laboratoire Jacques-Louis Lions, Universite Pierre et Marie Curie (巴黎六大), 博士后。

  ◆2007年1月 – 2008年8月, INRIA Saclay-Ile de France (法国国家信息与自动化研究院), 博士后。

  ◆2012年8月,2014年1月,2016年1月,香港中文大学数学系,访问教授。

  ◆2011年1月 – 2011年2月,巴黎六大Lions实验室,访问教授。

 

  教学

   本科生课程:数值分析, 线性代数, 微积分, 计算方法, 数值分析实验.

   研究生课程:高等数值代数, 量子信息与量子计算, 数值分析.

 

  教材

  向华, 李大美, 数值计算及其工程应用(全国工程专业学位研究生教育国家级规划教材), 清华大学出版社, 2015.

  邹秀芬, 陈绍林, 胡宝清, 向华, 数值计算方法学习指导书, 武汉大学出版社, 2008.

 

  研究论文

   P.Xie, H.Xiang, Y. Wei, A contribution to perturbation analysis for total least squares problems, Numerical Algorithms, 2017, DOI 10.1007/s11075-017-0285-1.

   L.Zhang, H.Xiang, Average entropy of a subsystem over a global unitary orbit of a mixed bipartite state, Quantum Information Processing, (2017) 16:112, DOI: 10.1007/s11128-017-1570-6.

   H. Xiang, J. Zou, Randomized algorithms for large-scale inverse problems with general Tikhonov regularizations, Inverse Problems, 31 (2015), 085008 (24pp). doi:10.1088/0266-5611/31/8/085008.

   J. Demmel, L. Grigori, M. Gu, H. Xiang, Communication avoiding rank revealing QR factorization with column pivoting, SIAM Journal on Matrix Analysis and Applications, 36(1), pp 55-89, 2015. See also UCB/EECS-2013-46 and LAWN 276.

   H. Shen, H. Xiang(*), Uzawa algorithms with variable relaxation for nonsymmetric generalized saddle point problems, Numerical Linear Algebra with Applications, 22 (2015), pp.1020–1038. DOI: 10.1002/nla.1988.

   B. Liu, H. Xiang(*), An approximate linear solver in least square support vector machine using randomized singular value decomposition, Wuhan University Journal of Natural Sciences 08/2015; 20(4):283-290. DOI:10.1007/s11859-015-1094-9.

   H. Xiang, F. Nataf, Two-level algebraic domain decomposition preconditioners using Jacobi–Schwarz smoother and adaptive coarse grid corrections, Journal of Computational and Applied Mathematics, 261 (2014), pp. 1-13.

   V. Dolean, P. Jolivet, F. Nataf, N. Spillane, H. Xiang, Two-level domain decomposition methods for highly heterogeneous Darcy equations, Connections with multiscale methods, Oil & Gas Science and Technology - Rev. IFP Energies nouvelles, Vol. 69 (2014), No. 4, pp. 731-752. DOI: 10.2516/ogst/2013206.

   C. Guo, H. Xiang(*), A note on the upper bound in SA AMG convergence analysis, Numerical Linear Algebra with Applications, Volume 21, Issue 3, (2014), pp. 399–402. DOI:10.1002/nla.1879.

   H. Xiang, J. Zou, Regularization with randomized SVD for large-scale discrete inverse problems, Inverse Problems, 29 (2013), 085008(23pp), doi:10.1088/0266-5611/29/8/085008.

   P. Have, R. Masson, F. Nataf, M. Szydlarski, H. Xiang, T. Zhao, Algebraic domain decomposition methods for highly heterogeneous problems, SIAM Journal on Scientific Computing, 35 (2013), pp. C284–C302.

   H. Diao, H. Xiang, Y. Wei, Componentwise condition numbers of Sylvester and Lyapunov equations, Numerical Linear Algebra and its Applications, 19 (4), pp.639-654, 2012. DOI:10.1002/nla.790.

   L. Grigori, J. Demmel, and H. Xiang, CALU: a communication optimal LU factorization algorithm, SIAM Journal on Matrix Analysis and Applications, 32 (2011), pp. 1317-1350. See also UCB-EECS-2010-29 and LAWN226.

   Frédéric Nataf, Hua Xiang, Victorita Dolean, Nicole Spillane, A coarse space construction based on local Dirichlet-to-Neumann maps, SIAM J. Sci. Comput., 33 (2011), pp. 1623-1642.

   Frederic Nataf, Hua Xiang, Victorita Dolean, A two level domain decomposition preconditioner based on local Dirichlet-to-Neumann maps, C. R. Acad. Sci. Paris, Ser. I, 348 (2010), pp. 1163-1167.

   Hua Xiang, Laura Grigori, Kronecker product approximation preconditioners for convection–diffusion model problems, Numer. Linear Algebra Appl., (17) 2010, pp. 691–712.

   Laura Grigori, Desire Nuentsa Wakamb, Hua Xiang (*), Saving flops in LU based shift-and-invert strategy, Journal of Computational and Applied Mathematics, 234 (2010), pp. 3216–3225.

   L. Grigori, J. Demmel, H. Xiang, Communication avoiding Gaussian elimination, SC’08, Proceedings of the 2008 ACM/IEEE conference on Supercomputing, 2008, pp.1-12.

   W. Kang, H. Xiang, Level-2 condition numbers for least squares solution of Kronecker product linear systems, International Journal of Computer Mathematics, 85(2008), pp. 827-841.

   H. Xiang, Y. Wei, On normwise structured backward errors for saddle point systems, SIAM Journal on Matrix Analysis and Applications, 29(2007), pp. 838-849.

   H. Xiang, Y. Wei, Structured mixed and componentwise condition numbers of some structured matrices, Journal of Computational Applied Mathematics, 202(2007), pp. 217-229.

   H. Zhang, H. Xiang, Y. Wei, Condition numbers for linear systems and Kronecker product linear systems with multiple right-hand sides, International Journal of Computer Mathematics, 84(2007), pp. 1805-1817.

   H. Xiang, Y. Wei, H. Diao, Perturbation analysis of generalized saddle point systems, Linear Algebra and its Applications, 419(2006), pp. 8-23.

   H. Xiang, A note on minimax representation for subspace distance and singular values, Linear Algebra and its Applications, 414(2006), pp. 470-473.

   Q. Liu, H. Xiang, V. P. Singh, A simulation model for unified interrill erosion and rill erosion on hillslopes, Hydrological Processes, 2006, 20(3), pp. 469-486.

   W. Kang, H. Xiang, Condition numbers with their condition numbers for the weighted Moore-Penrose inverse and the weighted least squares solution, J. Appl. Math. & Computing, 22(2006), pp. 95-112.

   Q. Liu, V. P. Singh, H. Xiang, Plot Erosion Model Using Gray Relational Analysis Method, J. Hydrologic Engineering, 2005, 10(4), pp. 288-294.

   H. Xiang, H. Diao, Y. Wei, On the perturbation bounds of Kronecker product linear systems and their level-2 condition numbers, Journal of Computational Applied Mathematics, 183 (2005), pp. 210-231.

   Y. Wei, Y. Cao, H. Xiang, A note on the componentwise perturbation bounds of matrix inverse and linear systems, Applied Mathematics and Computation, 169 (2005), pp. 1221-1236.

   Q. Liu, J. Li, L. Chen, H. Xiang, Overland flow and soil erosion dynamics (II): Soil erosion, Advances in Mechanics, 2004, 34(4), pp. 493-506 (in Chinese).

   Q. Liu, J. Li, L. Chen, H. Xiang, Overland flow and soil erosion dynamics (I): Overland flow, Advances in Mechanics, 2004, 34 (3), pp. 360-372 (in Chinese).

   Z. Gao, H. Xiang, Y. Shen, Perturbation finite volume method and high precision reconstruction, Computational Physics, 2004, 21(2), pp. 131-136 (in Chinese).

   H. Xiang, Q. Liu, J. Li, Influences of Slope Surface Conditions on the Runoff Generation, Journal of Hydrodynamics, series A, 2004, 19(6), pp. 774-782 (in Chinese).

 

  In preparation

  Kazufumi Ito, Hua Xiang, Jun Zou, An Inexact Uzawa algorithm for generalized saddle-point problems and its convergence, arXiv:1408.5547.

  Pengpeng Xie, Yimin Wei, Hua Xiang (*), Perturbation analysis and randomized algorithms for large-scale total least squares problems, arXiv:1401.6832.

   

  International Conferences

  ◆ Communication-avoiding matrix algorithms using tournament pivoting (joint work with James W. Demmel, Laura Grigori, and Ming Gu), A poster on the 5th International Conference on Numerical Algebra and Scientific Computing (NASC 2014), Tongji University, Shanghai, P.R. China, October 25-29, 2014.

  ◆ A communication optimal LU decomposition, May 3 - 14, 2010, CIMPA UNESCO Thematic School, Wuhan, P. R. China (invited speaker).

  ◆ Parallel sparse LU factorization with communication avoiding pivoting strategy, a talk given in the seminar at RICAM (Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences), July 22, 2008, Linz, Austria.

  ◆ A low latency approach for parallel sparse LU factorization, SIAM Conference on Parallel Processing for Scientific Computing (PP08), March 12-14, 2008, Atlanta, Georgia, USA.

  ◆ Communication avoiding dense QR and LU decompositions, Matrix Analysis and Applications (M2A07, in honor of Gérard Meurant for his 60th birthday), October 15-19, 2007, CIRM Luminy, Marseille, France, presented by L. Grigori.

  ◆ Kronecker product approximation preconditioner for convection-diffusion model problems, 2007 International Conference on Preconditioning Techniques for Large Sparse Matrix Problems in Scientific and Industrial Applications, July 9-12, 2007, Météopole, Toulouse, France.

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