线性鞍点问题的预处理与迭代算法
研究了线性鞍点问题的预处理技术与迭代算法;
利用矩阵的特殊结构和具体性质,
构造了一类新的快速迭代算法与预处理子, 分析了它们的代数性质.
对于参数化的不精确Uzawa迭代算法,
给出了最佳参数的计算公式, 以及相应的最优收敛速度.
对于具有分块二阶结构的矩阵, 给出了HSS算法最优参数的计算公式,
并估计出了HSS算法关于一般非对称矩阵的最优参数值.
提出了求解非对称代数黎卡提方程的交替线性化隐式迭代算法, 证明了这类
算法的单调收敛性质, 并用数值结果表明了这类新算法的可行性和有效性.
2006年正式发表的论文如下:
- A shift-splitting preconditioner for non-Hermitian
positive definite matrices,
Journal of Computational Mathematics,
24:4(2006), 539-552.
(With Yang-Feng Su and Jun-Feng Yin)
- Alternately linearized implicit iteration methods
for the minimal nonnegative solutions
of nonsymmetric algebraic Riccati equations,
Numerical Linear Algebra with Applications,
13:8(2006), 655-674.
(With Xiao-Xia Guo and Shu-Fang Xu)
- Convergence analysis of two-stage waveform relaxation method
for the initial value problems,
Applied Mathematics and Computation,
172:2(2006), 797-808.
(With Jing Wang)
- Structured preconditioners for nonsingular matrices of
block two-by-two structures,
Mathematics of Computation,
75:254(2006), 791-815.
- Restrictive preconditioners for conjugate gradient methods
for symmetric positive definite linear systems,
Journal of Computational and Applied Mathematics,
187:2(2006), 202-226.
(With Zeng-Qi Wang)
- New preconditioners for saddle point problems,
Applied Mathematics and Computation,
172:2(2006), 762-771.
(With Jian-Yu Pan and Michael K. Ng)
- Optimal parameter in
Hermitian and skew-Hermitian splitting method
for certain two-by-two block matrices,
SIAM Journal on Scientific Computing,
28:2(2006), 583-603.
(With Gene H. Golub and Chi-Kwong Li)
- Two-step iterative methods for solving the stationary
convection-diffusion equation with a small parameter
at the highest derivative on a uniform grid,
Computational Mathematics and Mathematical Physics,
46:2(2006), 282-293.
(With L.A. Krukier and T.S. Martynova)
- A modified damped Newton method for linear complementarity problems,
Numerical Algorithms,
42:3-4(2006), 207-228.
(With Jun-Liang Dong)
- Iterative orthogonal direction methods
for Hermitian minimum norm solutions of
two consistent matrix equations,
Numerical Linear Algebra with Applications,
13:10(2006), 801-823.
(With Yuan-Bei Deng and Yong-Hua Gao)
- A Lanczos-based projection method for symmetric indefinite linear systems,
Proceedings of the Seventh China-Japan Seminar
on Numerical Mathematics,
Shi Zhong-Ci and Okamoto, H. eds., Science Press of China,
Beijing/New York, 1-18(2006).
(With Xue-Bin Chi and Zeng-Qi Wang)
2006年参加国际学术会议, 并做邀请报告如下:
- Iterative splitting methods for nonsymmetric
algebraic Riccati equations,
The Second International Conference
on Structured Matrices,
Hong Kong Baptist University, Hong Kong, P.R. China,
June 8--11, 2006.
(30 minutes)
- Iterative splitting methods for nonsymmetric
algebraic Riccati equations,
The First China-Japan-Korea Joint Conference
on Numerical Mathematics,
Sapporo Convention Center, Hokkaido, Japan,
August 3--7, 2006.
(40 minutes)
- Iterative splitting methods for nonsymmetric
algebraic Riccati equations,
International Seminar on
Applied Mathematics for Real World Problems,
Ryutsu-Keizai University, Tokyo, Japan,
September 13--14, 2006.
(45 minutes)
2006年国际学术访问如下:
- Department of Mathematics,
The University of Hong Kong,,
Hong Kong, P.R. China, July 27--30, 2006.
(Wai-Ki Ching)
- Department of Mathematics,
Hong Kong Baptist University,
Hong Kong, P.R. China, March 1--31, 2006.
(Michael Kwok-Po Ng)
- National Institute of Informatics,
Tokyo, Japan, August 8--12, 2006.
(Ken Hayami)