线性鞍点问题的预处理与迭代算法
提出了求解线性鞍点问题的加速HSS（AHSS）算法，确定了它的最优参数和相应的最佳收敛因子；理论分析表明，
该算法是迄今为止关于线性鞍点问题的最快迭代算法；
数值结果表明，AHSS算法无论作为迭代法还是作为预处理子均是可行和十分有效的.
建立了Burgers方程经Sinc-Galerkin离散所产生的结构化非线性代数方程组的有效迭代算法和收敛理论.
研究了一般非线性方程组的Newton-GMRES算法及其收敛性.
2007年正式发表的论文如下:
- A globally convergent Newton-GMRES method for large sparse
systems of nonlinear equations,
Applied Numerical Mathematics,
57:3(2007), 235-252.
(With Heng-Bin An)
- Splitting iteration methods for non-Hermitian positive definite
systems of linear equations,
Hokkaido Mathematical Journal,
36:4(2007), 801-814.
- Modified Bernoulli iteration methods
for quadratic matrix equation,
Journal of Computational Mathematics,
25:5(2007), 498-511.
(With Yong-Hua Gao)
- On successive overrelaxation acceleration of
the Hermitian and skew-Hermitian splitting
iterations,
Numerical Linear Algebra with Applications,
14:4(2007), 319-335.
(With Gene H. Golub and Michael K. Ng)
- Accelerated Hermitian and skew-Hermitian splitting
iteration methods for saddle-point problems,
IMA Journal of Numerical Analysis,
27:1(2007), 1-23.
(With Gene H. Golub)
- Convergence properties of preconditioned
Hermitian and skew-Hermitian splitting methods
for non-Hermitian positive semidefinite matrices,
Mathematics of Computation,
76:257(2007), 287-298.
(With Gene H. Golub and Chi-Kwong Li)
- On preconditioned iterative methods for Burgers equations,
SIAM Journal on Scientific Computing,
29:1(2007), 415-439.
(With Yu-Mei Huang and Michael K. Ng)
2007年参加国际学术会议, 并做邀请报告如下:
- On Hermitian and skew-Hermitian splitting iteration methods,
International Workshop on Matrices and Operators,
The University of Hong Kong, Hong Kong, P.R. China,
April 13--14, 2007.
(45 minutes)
- On Hermitian and skew-Hermitian splitting iteration methods,
The 36th Numerical Analysis Symposium,
Wel Hotel and Resorts, Yugawara, Japan,
June 19--21, 2007.
(40 minutes)
- Recent advances on splitting preconditioners
for solving saddle point problems,
The Second International Summer School on
Numerical Linear Algebra,
School of Mathematics and Statistics,
Lanzhou University, Lanzhou, P.R. China,
July 25--August 6, 2007.
(30 minutes)
- Recent advances on splitting preconditioners
for solving saddle point problems,
The 12th Russia School-Seminar
on Modern Problems in Mathematical Modelling,
Abrau-Durso, Novorossisk, Russia,
September 17--22, 2007.
(40 minutes)
- Recent Advances on Matrix Splittings
for Solving Saddle Point Problems,
International Workshop on Applied Mathematics
and Computational Science,
The University of Electro-Communications, Tokyo, Japan,
September 25--28, 2007.
(45 minutes)
- Recent Advances on Matrix Splittings
for Solving Saddle Point Problems,
Workshop on Solution Methods
for Saddle Point Systems,
Hong Kong Baptist University, Hong Kong, P.R. China,
October 31, 2007.
(45 minutes)
2007年国际学术访问如下:
- School of Mathematical Sciences,
Xiamen University,
Xiamen, P.R. China,
January 30--February 12, 2007,
March 15--28, 2007.
(Lin-Zhang Lu)
- National Institute of Informatics,
Tokyo, Japan, June 10--22, 2007.
(Ken Hayami)
- Seminar for Applied Mathematics,
The Swiss Federal Institute of Technology
in Zurich (ETH Zurich),
Zurich, Switzerland, July 14--21, 2007.
(Martin H. Gutknecht)
- The South-Russian Regional Center of Informatization,
Southern Federal University,
Rostov-on-Don, Russia,
September 5--20, 2007.
(Lev A. Krukier)
- Department of Mathematics,
Hong Kong Baptist University,
Hong Kong, P.R. China, October 2--November 1, 2007.
(Michael Kwok-Po Ng)