数值代数，科学计算

      梁兆正，男，副教授，硕士研究生导师。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。主要研究兴趣为产生于不同应用背景的大规模结构代数系统的快速算法和预处理技术，主持完成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，现主持中央高校基本科研业务费一项，获批甘肃省青年科技基金项目一项。

现指导专业学位研究生1名，协助指导博士和硕士研究生若干。

      在 Adv. Comput. Math.，BIT Numer. Math., Appl. Numer. Math., Numer. Algor., J. Comput. Appl. Math., Numer. Linear Algebra Appl., Linear Algebra Appl.  等SCI期刊发表科研论文多篇。
      
近5年发表的部分SCI论文：
1.  Z.-Z. Liang*, Y. Dou. Fast rotated BSOR method for block two-by-two linear systems with application to PDE-constrained optimal control problems, BIT Numerical Mathematics, 62: 1175-1206, 2022.
2.  Z.-Z. Liang*, O. Axelsson. Exact inverse solution techniques for a class complex valued block two-by-two linear systems, Numerical Algorithms, 90: 79-98, 2022.
3.  Z.-Z. Liang*, G.-F. Zhang. Robust preconditioning techniques for multiharmonic finite element method with application to time-periodic parabolic optimal control problems, Advances in Computational Mathematics, 47: 67, 2021.
4.  Z.-Z. Liang*, Y. Dou. Efficient preconditioning techniques for velocity tracking of Stokes control problem, Applied Numerical Mathematics, 165: 322-338, 2021.
5.  Z.-Z. Liang*, G.-F. Zhang, On Chebyshev accelerated iteration methods for two-by- two block linear systems, Journal of Computational and Applied Mathematics, 391: 113449, 2021.
6.  Z.-Z. Liang*, O. Axelsson, G.-F. Zhang. Efficient iterative solvers for a complex valued two-by-two block linear system with application to parabolic optimal control problems, Applied Numerical Mathematics, 152: 422-445, 2020.
7.  Z.-Z. Liang*, G.-F. Zhang. Robust additive block triangular preconditioners for block two-by-two linear systems, Numerical Algorithms, 82:503-537, 2019.
8.  Z.-Z. Liang*, G.-F. Zhang. Alternating positive semidefinite splitting preconditioners for double saddle point problems, Calcolo, 56: 26, 2019.
9.  Y. Dou, Z.-Z. Liang*, A class of block alternating splitting implicit iteration methods for double saddle point linear systems, Numerical Linear Algebra with Applications, 30(1): e2455, 2022.
10. O. Axelsson*, Z.-Z. Liang. Parameter modified versions of preconditioning and iterative inner product free refinement methods for two-by-two block matrices, Linear Algebra and its Applications, 582: 403-429, 2019.
11. O. Axelsson, Z.-Z. Liang*, J. Kruzik, D. Horak. Inner product free iterative solution and elimination methods for linear systems of a three-by-three block matrix form, Journal of Computational and Applied Mathematics, 383:113117, 2021.
12. O. Axelsson, Z.-Z. Liang*. A note on preconditioning methods for time-periodic eddy current optimal control problems, Journal of Computational and Applied Mathematics, 352: 262-277, 2019.
13. L. Zhang, G.-F. Zhang*, Z.-Z. Liang, Tensorized low-rank circulant preconditioners for multilevel Toeplitz linear systems from high-dimensional fractional Riesz equations, Computers and Mathematics with Applications, 110: 64-76, 2022.
14. L. Zhang, G.-F. Zhang*, Z.-Z. Liang, Fast preconditioned iterative methods for fractional Sturm-Liouville equations, Numerical Methods for Partial Differential Equations, 37: 2278-2295, 2021.
15. R.-X. Li, G.-F. Zhang*, Z.-Z. Liang, Fast solver of optimal control problems constrained by Ohta-Kawasaki equations, Numerical Algorithms, 85: 787-809, 2020.

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（国家自然科学基金青年基金，11801242）, 主持；
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；
3. 高维分数阶PDE约束优化问题的快速迭代算法研究（中央高校基本科研业务费，lzujbky-2022-05），主持；
4. 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;
5. 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。

  指导完成国家级和校级大学生创新创业训练计划各1项，获评优秀指导教师。

社会工作：
      担任 Appl. Numer. Math., Numer. Algor., J. comput. Appl. Math., Appl. Math Lett., Comput. Math. Appl., Numer. Math. Theor. Meth. Appl., Int. J. Comput. Math., Appl. Math. Comput. 等多类SCI 期刊的审稿人。