鞍点问题与矩阵方程的迭代算法与收敛理论
对于非Hermitian正定的线性代数方程组，深入研究了HSS迭代算法的高效实施策略，
建立了适合于实际计算的不精确变型并进行了相应的理论分析. 对于线性鞍点问题，
我们深入研究了参数化的不精确Uzawa迭代算法的收敛与代数性质，
给出了最佳参数的计算公式以及相应的最优收敛速度.
对于中子输运理论中的一类特殊的代数黎卡提方程，我们构造了简单而快速的向量化迭代算法，
并建立了算法的单调收敛理论.
2008年正式发表的论文如下:
- Convergence conditions for splitting iteration methods for
non-Hermitian linear systems,
Linear Algebra and Its Applications,
428:2-3(2008), 453-468.
(With Li Wang)
- Fast iterative schemes for nonsymmetric algebraic Riccati equations
arising from transport theory,
SIAM Journal on Scientific Computing,
30:2(2008), 804-818.
(With Yong-Hua Gao and Lin-Zhang Lu)
- On inexact Hermitian and skew-Hermitian splitting
methods for non-Hermitian positive definite linear systems,
Linear Algebra and Its Applications,
428:2-3(2008), 413-440.
(With Gene H. Golub and Michael K. Ng)
- Several splittings for non-Hermitian linear systems,
Science in China, Series A: Mathematics,
51:8(2008), 1339-1348.
- On parameterized inexact Uzawa methods
for generalized saddle point problems,
Linear Algebra and Its Applications,
428:11-12(2008), 2900-2932.
(With Zeng-Qi Wang)
- The restrictively preconditioned conjugate gradient methods
on normal residual for block two-by-two linear systems,
Journal of Computational Mathematics,
26:2(2008), 240-249.
(With Jun-Feng Yin)
2008年参加国际学术会议, 并做邀请报告如下:
- Restrictively Preconditioned Conjugate Gradient Methods,
Remembering Gene Golub Around the World on February 29,
Hong Kong Baptist University, Hong Kong, P.R. China,
February 29, 2008.
(30 minutes)
- On Preconditioned Iterative Methods for Burgers Equations,
The Spring Meeting of the Union of Research Activity Groups
of Japan Society of Industrial and Applied Mathematics,
Tokyo Metropolitan University, Tokyo, Japan,
March 8--9, 2008.
(30 minutes, Plenary Speaker)
- Recent Advances on Matrix Splittings for Solving Saddle Point Problems,
The AMSS-PolyU Joint Research Workshop,
The Hong Kong Polytechnic University,
Hong Kong, P.R. China,
June 27, 2008.
(30 minutes)
- Restrictively Preconditioned Conjugate Gradient Methods,
International Conference on Matrix Theory
and its Applications,
Chinese Linear Algebra Society and
The Normal College of Shanxi University, Taiyuan,
P.R. China,
July 16--20, 2008.
(45 minutes)
- On Preconditioned Iterative Methods for Burgers Equations,
The Second China-Japan-Korea Joint Conference
on Numerical Mathematics,
Weihai, Shangdong Province, P.R. China,
August 25--29, 2008.
(35 minutes)
- On Preconditioned Iterative Methods for Burgers Equations,
International Workshop on Numerical Analysis
and Scientific Computing,
Southern Federal University, Rostov-on-Don, Russia,
October 13--17, 2008.
(45 minutes, Plenary Speaker)
- Structured Splitting Iterative Methods for Mildly Nonlinear Systems,
RIMS Workshop on Numerical Analysis--Theory,
Methods and Applications,
Research Institute for Mathematical Sciences, Kyoto University,
Kyoto, Japan,
November 12--14, 2008.
(45 minutes)
- Vectorized Iteration Methods for Algebraic Riccati Equations
from Transport Theory,
The Third International Conference
on Scientific Computing and Partial Differential Equations,
Hong Kong Baptist University, Hong Kong, P.R. China,
December 8--12, 2008.
(25 minutes)
- Vectorized Iteration Methods for Algebraic Riccati Equations
from Transport Theory,
The First International Conference
on Frontiers in Computational Mathematics,
Guilin, Guangxi Zhuang Autonomous Region, P.R. China,
December 15--17, 2008.
(30 minutes)
2008年国际学术访问如下:
- National Institute of Informatics,
Tokyo, Japan, March 1--10 and November 11--20, 2007.
(Ken Hayami)
- The AMSS-PolyU Joint Research Institute
for Engineering and Management Mathematics,
The Hong Kong Polytechnic University,
Hong Kong, P.R. China.
June 23--28, 2008.
(Xiao-Jun Chen)
- The South-Russian Regional Center of Informatization,
Southern Federal University,
Rostov-on-Don, Russia,
October 13--19, 2008.
(Lev A. Krukier)