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梁兆正

兰州大学数学与统计学院     讲师   梁兆正

研究方向
数值线性代数
个人简历
梁兆正,男,讲师,2017年12月博士毕业于兰州大学数学与统计学院,获得计算数学博士学位,导师为张国凤教授。2016年9月-2017年9月,瑞典乌普萨拉大学信息技术与计算科学学院,联合培养博士研究生,导师为Maya Neytcheva教授。主要研究产生于不同应用背景的结构线性系统的有效迭代方法和预处理子的设计,现主持在研国家自然科学基金青年基金项目和中央高校基本科研业务费项目各一项。
教学及指导学生情况
发表论文及专著
[1] Z.-Z. Liang, G.-F. Zhang, A class of modified DPSS preconditioners for generalized saddle-point linear systems, Comput. Appl. Math., https://doi.org/10.1007/s40314-019-0844-2, 2019.
[2] Z.-Z. Liang, G.-F. Zhang, Robust additive block triangular preconditioners for block two-by-two linear systems, Numer. Algorithms, https://doi.org/10.1007/s11075-018-0611-2, 2019.
[3] O. Axelsson, Z.-Z. Liang, A note on preconditioning methods for time-periodic eddy current optimal control problems, J. Comput. Appl. Math., 352: 262--277, 2019.
[4] O. Axelsson, M. Neytcheva, Z.-Z. Liang, Parallel solution methods and preconditioners for evolution equations, Math. Model. Anal., 23(2): 287--308, 2018. 
[5] R.-X. Li, Z.-Z. Liang, G.-F. Zhang, L.-D. Liao, L. Zhang, A note on preconditioner for the Ohta–Kawasaki equation, Appl. Math. Lett., 85: 132--138, 2018.
[6] Z.-Z. Liang, O. Axelsson, M. Neytcheva, A robust structured preconditioner for time-harmonic parabolic optimal control problems, Numer. Algorithms, 79:575--596, 2018. 
[7] Z.-Z. Liang, G.-F. Zhang, Parameterized approximate block LU preconditioners for generalized saddle point problems, J. Comput. Appl. Math., 302:211--223, 2018.
[8] Z.-Z. Liang, G.-F. Zhang. Semi-convergence analysis of preconditioned deteriorated PSS iteration method for singular saddle point problems, Numer. Algorithms., 79(2): 379--404, 2018. 
[9] Z.-Z. Liang, G.-F. Zhang. On nonlinear inexact Uzawa algorithms for stabilized saddle point problems, Comput. Appl. Math., 37(2): 2129--2151, 2018.
[10] Z.-Z. Liang, G.-F. Zhang. Variants of the deteriorated PSS preconditioner for saddle point problems, Comput. Math. Appl., 75(8): 3024--3046, 2018. 
[11] Z.-Z. Liang, G.-F. Zhang. Convergence behavior of generalized parameterized Uzawa method for singular saddle-point problems. J. Comput. Appl. Math., 311:293--305, 2017. 
[12] Z.-Z. Liang, G.-F. Zhang. Analysis of the relaxed deteriorated PSS preconditioner for singular saddle point linear systems, Appl. Math. Comput., 305: 308--322, 2017. 
[13] Z.-Z. Liang, G.-F. Zhang. On SSOR iteration method for a class of block two-by-two linear systems, Numer. Algorithms, 71: 655--671, 2016. 
[14] Z.-Z. Liang, G.-F. Zhang. Augmented block splitting preconditioner for singular saddle point problems, Appl. Math. Lett., 56: 34--41, 2016. 
[15] Z.-Z. Liang, G.-F. Zhang. Variants of the accelerated parameterized inexact Uzawa method for saddle-point problems, BIT Numer. Math., 56:523--542, 2016. 
[16] Z.-Z. Liang, G.-F. Zhang. SIMPLE-like preconditioners for saddle point problems from the steady Navier-Stokes equations. J. Comput. Appl. Math., 302:211--223, 2016. 
[17] Z.-Z. Liang, G.-F. Zhang. Two new variants of the HSS preconditioners for regularized saddle point problems. Comput. Math. Appl., 72 (3): 603--619, 2016. 
[18] Z.-Z. Liang, G.-F. Zhang. PU-STS method for non-Hermitian saddle-point problems, Appl. Math. Lett., 46: 1--6, 2015.
[19] Z.-Z. Liang, G.-F. Zhang. On PSS-based constraint preconditioners for singular nonsymmetric saddle point problems, Comput. Math. Appl., 69: 455--465, 2015.
[20] Z.-Z. Liang, G.-F. Zhang. Semi-convergence analysis of the GPIU method for singular non- symmetric saddle-point problems, Numer. Algorithms, 70: 151--169, 2015.
项目成果
1. 时间依赖PDE约束优化问题的高效预处理和迭代求解技术研究(国家自然科学基金,11801242), 主持人;
2. 几类鞍点结构线性系统的快速算法研究(中央高校基本科研业务费,lzujbky-2018-31),主持人;
3. 一类大规模结构线性鞍点问题的高效算法与理论(国家自然科学基金,11271174),参与者;
4. 两类PDE控制离散矩阵的预处理及快速计算(国家自然科学基金,11771193),参与者。
荣誉、获奖
2013	硕士研究生国家奖学金
2015	博士研究生国家奖学金
社会工作
其它信息

作者:梁兆正