非对称代数方程组的迭代算法
研究了求解弱非线性代数方程组的并行多分裂二级迭代算法
对于对称正定矩阵类的收敛性理论。
研究了对称线性代数方程组的加型和乘型分裂迭代算法
的收敛性理论。
研究了对称 Sinc-Galerkin 方程组的组合预处理子
的代数构造与理论性质。
对于一般非对称线性代数方程组, 构造了有效的
对称与反对称分裂迭代算法, 并建立了算法的
收敛理论。
同时, 还研究了若干特殊的矩阵方程的数学
性质和直接解法。
2003年正式发表的论文如下:
- On the convergence of additive and multiplicative
splitting iterations for systems of linear equations,
Journal of Computational and Applied Mathematics,
154(2003), 195-214.
- Convergence theorems for parallel multisplitting
two-stage iterative methods for mildly nonlinear systems,
Linear Algebra and Its Applications,
362(2003), 237-250. (With C.-L. Wang)
- Least-squares solution of AXB=D
over symmetric positive semidefinite matrices X,
Journal of Computational Mathematics,
21:2(2003), 175-182. (With A.-P. Liao)
- A hybrid preconditioner of banded matrix approximation
and alternating direction implicit iteration
for symmetric Sinc-Galerkin linear systems,
Linear Algebra and Its Applications,
366(2003), 317-335. (With M.K. Ng)
- Hermitian and skew-Hermitian splitting methods for
non-Hermitian positive definite linear systems,
SIAM Journal on
Matrix Analysis and Applications,
24(2003), 603-626. (With G.H. Golub and M.K. Ng)
- On the convergence of parallel nonstationary
multisplitting iteration methods,
Journal of
Computational and Applied Mathematics,
159(2003), 1-11.
- Asymptotically optimal successive overrelaxation methods
for systems of linear equations,
Journal of Computational Mathematics,
21:5(2003), 603-612.
(With X.-B. Chi)
- An algebraic convergence theorem for the multiplicative
Schwarz iteration,
Numerical Mathematics,
A Journal of Chinese Universities (English Series),
12:Supplememnt(2003), 179-182.
- Weak convergence theory of quasi-nonnegative splittings
for singular matrices,
Applied Numerical Mathematics,
47:2(2003), 75-89.
(With L. Wang and J.-Y. Yuan)
- Restrictively preconditioned conjugate gradient methods for
systems of linear equations,
IMA Journal of Numerical Analysis,
23:4(2003), 561-580.
(With G.-Q. Li)
- Preconditioners for nonsymmetric block
Toeplitz-like-plus-diagonal linear systems,
Numerische Mathematik,
96:2(2003), 197-220.
(With M.K. Ng)
- A class of asynchronous parallel multisplitting relaxation methods
for the large sparse linear complementarity problems,
Journal of Computational Mathematics,
21:6(2003), 773-790.
(With Y.-G. Huang)
- Column-decomposed relaxation methods for
the overdetermined systems of linear equations,
International Journal of Applied Mathematics,
13:1(2003), 71-82.
(With C.-H. Jin)
2003年参加国际国内学术会议, 并做邀请报告如下:
- Asynchronous parallel multisplitting relaxation methods
for linear complementarity problems,
International Conference
on Parallel Algorithms and Computing Environments,
The Chinese University of Hong Kong, P.R. China,
October 8--11, 2003.
(30 minutes)