研究了一类大型稀疏弱非线性代数方程组的异步并行算法。
对于一般线性代数方程组, 揭示了KRYLOV子空间
迭代算法的收敛性质与系数矩阵的特征值, 特征向量, 以及最大JORDAN块的阶数之间
的内在关系, 从而进一步完善了子空间迭代算法的收敛理论。
获得国务院政府特殊津贴 (2000年6月)。
2000年正式发表的论文如下:
- A class of asynchronous parallel iterations for the systems of
nonlinear algebraic equations,
Computers and Mathematics with Applications,
39:7-8(2000), 81-94.
- Sharp error bounds of some Krylov subspace methods for
non-Hermitian linear systems,
Applied Mathematics and Computation,
109:2-3(2000), 273-285.
2000年参加国际国内学术会议, 并做邀请报告如下:
- Matrix multisplitting methods and theories,
The Second China-Sweden Workshop on
Numerical Partial Differential Equations,
Hong Kong University of Science and Technology,
Hong Kong, P.R. China, January 10-12, 2000. (45 minutes)
- Parallel Chaotic Multisplitting Iterative Methods
for the Large Sparse Linear Complementarity Problem,
The Second Sino-Italian
Symposium on Computational and
Applied Mathematics and The Fifth Congress of Italian Society for
Applied and Industrial Mathematics (SIMAI),
Italian Society for Applied and Industrial Mathematics (SIMAI),
Ischia, Italy, June 5-9, 2000. (30 minutes)
- A regularized conjugate gradient method for
symmetric positive definite system of linear equations,
The Fifth China-Japan Joint
Seminar on Numerical Mathematics,
Shanghai Jiaotong University,
Shanghai, P.R. China, August 21-25, 2000. (60 minutes)
- 矩阵多分裂算法与理论,
第八届全国高等学校计算数学学术会议,
武汉大学, 武汉, 2000年10月16-20日. (30 分钟)
2000年学术讲座如下:
- Parallel multisplitting iteration methods
for algebraic systems of linear equations,
Department of Mathematics,
Lanzhou University,
Lanzhou, P.R. China,
May 8-16, 2000.
(9 \times 120 minutes)