研究工作概要
给出了Meany不等式的下界估计和上界的更为精细的估计，
并运用其分析了行处理方法的收敛性质；
提出了有效求解大规模稀疏线性互补问题的并行矩阵多分裂迭代方法，
并建立了其收敛理论；对于离散的分布式最优控制问题，
构造出了预处理MHSS迭代方法，建立了其收敛理论，
给出了相应的预处理子的代数性质，并讨论了其数值实现。
此外，还给出了分块二阶矩阵非奇异的充要条件。
2013年正式发表的论文如下:
- Additive block diagonal preconditioning for block
two-by-two linear systems of skew-Hamiltonian
coefficient matrices,
Numerical Algorithms,
62:4(2013), 655-675.
(With Fang Chen and Zeng-Qi Wang)
- On the Meany inequality with applications
to convergence analysis of several row-action
iteration methods,
Numerische Mathematik,
124:2(2013), 215-236.
(With Xin-Guo Liu)
- On nonsingularity of block two-by-two matrices,
Linear Algebra and its Applications,
439:8(2013), 2388-2404.
(With Zheng-Jian Bai)
- Rotated block triangular preconditioning based on PMHSS,
Science China Mathematics,
56:12(2013), 2523-2538.
- Modulus-based synchronous two-stage multisplitting
iteration methods for linear complementarity problems,
Numerical Algorithms,
62:1(2013), 59-77.
(With Li-Li Zhang)
- Modulus-based synchronous multisplitting
iteration methods for linear complementarity problems,
Numerical Linear Algebra with Applications,
20:3(2013), 425-439.
(With Li-Li Zhang)
- Preconditioned MHSS iteration methods for
a class of block two-by-two linear systems
with applications to distributed control problems,
IMA Journal of Numerical Analysis,
33:1(2013), 343-369.
(With Michele Benzi, Fang Chen and Zeng-Qi Wang)
- Eigenvalue estimates for saddle point matrices
of Hermitian and indefinite leading blocks,
Journal of Computational
and Applied Mathematics,
237:1(2013), 295-306.
- Block-triangular preconditioning methods for
linear third-order ordinary differential equations
based on reduced-order sinc discretizations,
Japan Journal of Industrial
and Applied Mathematics,
30:3(2013), 511-527.
(With Zhi-Ru Ren)