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。

2004年正式发表的论文如下:

- A class of nested iteration schemes for linear systems
with a coefficient matrix with a dominant
positive definite symmetric part,
Numerical Algorithms,
35:2-4(2004), 351-372. (With O. Axelsson and S.-X. Qiu)

- Broyden method for nonlinear equation in several variables,
Mathematica Numerica Sinica,
26:4(2004), 385-400. (With H.-B. An)

- On the convergence of waveform relaxation methods
for linear initial value problems,
Journal of Computational Mathematics,
22:5(2004), 681-698. (With J.-Y. Pan)

- Combinative preconditioners of
modified incomplete Cholesky factorization and
Sherman-Morrison-Woodbury update for
self-adjoint elliptic Dirichlet-periodic
boundary value problems,
Journal of Computational Mathematics,
22:6(2004), 833-856. (With G.-Q. Li and L.-Z. Lu)

- Preconditioned Hermitian and skew-Hermitian splitting
methods for non-Hermitian positive semidefinite linear systems,
Numerische Mathematik,
98:1(2004), 1-32. (With G.H. Golub and J.-Y. Pan)

- Skew-Hermitian triangular splitting iteration methods
for non-Hermitian positive definite linear systems of
strong skew-Hermitian parts,
BIT Numerical Mathematics,
44:2(2004), 363-386. (With L. Wang)

- Construction and analysis of structured preconditioners
for block two-by-two matrices,
Journal of Shanghai University (English Edition),
8:4(2004), 397-405.

- Block triangular and skew-Hermitian splitting iteration methods for
positive definite linear systems,
International Conference on Scientific Computing
in Petroleum Industry,
Jiuhua SPA and Resort, Beijing, P.R. China,
August 4-7, 2004.
(30 minutes)

- Splitting iteration methods for non-Hermitian positive definite linear systems, The Seventh China-Japan Joint Seminar on Numerical Mathematics and Scientific Computing, Zhangjiajie, Hunan Province, P.R. China, August 16-20, 2004. (60 minutes)

- Hermitian and skew-Hermitian splitting methods
for non-Hermitian positive definite linear systems,
Department of Mathematics,
Delaware State University,
Dover, USA,
June 14, 2004.
(50 minutes)

- Hermitian and skew-Hermitian splitting methods
for non-Hermitian positive definite linear systems,
Faculty of Applied Mathematics,
University of
Electronic Science and Technology of China,
Chengdu, P.R. China,
July 2, 2004.
(50 minutes)

- Splitting iteration methods for
non-Hermitian positive definite linear systems,
Department of Mathematics,
Fudan University,
Shanghai, P.R. China,
October 22, 2004.
(60 minutes)

- Splitting iteration methods for
non-Hermitian positive definite linear systems,
Department of Mathematics,
The East China Normal University,
Shanghai, P.R. China,
November 3, 2004.
(60 minutes)

- Splitting iteration methods for
non-Hermitian positive definite linear systems,
College of Sciences,
Nanjing University of Aeronautics and Astronautics,
Nanjing, P.R. China,
November 22, 2004.
(60 minutes)

- Solutions of linear systems of block two-by-two structures,
College of Sciences,
Nanjing University of Aeronautics and Astronautics,
Nanjing, P.R. China,
November 23, 2004.
(60 minutes)

- Solutions of linear systems of block two-by-two structures,
School of Mathematics and Computer Science,
Nanjing Normal University,
Nanjing, P.R. China,
November 24, 2004.
(60 minutes)