预处理与迭代算法
研究了求解线性与非线性代数方程组的预处理与迭代算法。
研究了常微分方程初值问题的波型松弛迭代算法
及其收敛理论。
2005年正式发表的论文如下:
- Directional secant method for nonlinear equations,
Journal of Computational and Applied Mathematics,
175:2(2005), 291-304.
(With H.-B. An)
- On alternating splitting waveform relaxation method
and its successive overrelaxation acceleration,
Computers and Mathematics with Applications,
49:2-3(2005), 157-170.
(With J.-Y. Pan and M.K. Ng)
- Block triangular and skew-Hermitian splitting
methods for positive definite linear systems,
SIAM Journal on Scientific Computing,
26:3(2005), 844-863.
(With G.H. Golub, L.-Z. Lu and J.-F. Yin)
- Two-step waveform relaxation methods
for implicit linear initial value problems,
Numerical Linear Algebra with Applications,
12:2-3(2005), 293-304. (With J.-Y. Pan and M.K. Ng)
- Least squares symmetric and skew-symmetric solutions of the
matrix equation AXA^T + BYB^T = C with the least norm,
Mathematica Numerica Sinica,
27:1(2005), 81-95. (With A.-P. Liao)
- Best approximate solution of matrix equation AXB + CYD = E,
SIAM Journal on Matrix Analysis and Applications,
27:3(2005), 675-688. (With A.-P. Liao and Y. Lei)
- NGLM: A globally convergent Newton-GMRES method,
Mathematica Numerica Sinica,
27:2(2005), 151-174. (With H.-B. An)
- On the minimal nonnegative solution
of nonsymmetric algebraic Riccati equation,
Journal of Computational Mathematics,
23:3(2005), 305-320. (With X.-X. Guo)
- On inexact preconditioners for nonsymmetric matrices,
SIAM Journal on Scientific Computing,
26:5(2005), 1710-1724.
(With M.K. Ng)
- On generalized successive overrelaxation methods for augmented linear systems,
Numerische Mathematik,
102:1(2005), 1-38.
(With B.N. Parlett and Z.-Q. Wang)
- On efficient variants and global convergence of the Newton-GMRES method,
Journal of Numerical Methods
and Computer Applications,
26:4(2005), 291-300.
(With H.-B. An)
2005年参加国际学术会议, 并做邀请报告如下:
- Solutions of linear systems of block two-by-two structures,
International Workshop on Optimization
and Data Technology with Applications,
The Graduate University of Chinese Academy of Sciences,
Beijing, P.R. China,
March 25, 2005.
(30 minutes)
- Splitting iteration methods for
non-Hermitian positive definite linear systems,
First International Workshop on Matrix Analysis,
Beijing Normal University, Beijing, P.R. China,
June 9--10, 2005.
(45 minutes)
- Splitting iteration methods for
non-Hermitian positive definite linear systems,
International Workshop on
Fast Integral and Symplectic Methods,
Morningside Center of Mathematics, Beijing, P.R. China,
May 8--July 20, 2005.
(120 minutes)
- Splitting iteration methods for
saddle point linear systems,
Numerical Linear Algebra Workshop and
International Conference on Super-Resolution Imaging,
The University of Hong Kong, Hong Kong, P.R. China,
August 28--September 2, 2005.
(45 minutes)
- Splitting iteration methods for
saddle point linear systems,
Applied Linear Algebra--in Honor to Professor Richard S. Varga,
Palic, Serbia and Montenegro,
October 13--15, 2005.
(45 minutes)
- Splitting iteration methods for
non-Hermitian positive definite linear systems,
RIMS Workshop on Computational Science
-Foundamental and Emerging Technology,
Research Institute for Mathematical science,
Kyoto University, Kyoto, Japan,
November 30--December 2, 2005.
(45 minutes)
- Splitting iteration methods for
saddle point linear systems,
Joint Workshop on Computational Chemistry and Numerical Analysis
(CCNA2005),
Tokyo, Japan,
December 5--6, 2005.
(30 minutes)