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杨爱利

杨爱利,男,理学博士,副教授,硕士生导师,海南省拔尖人才,美国数学会评论员。

Email: yangaili@hainnu.edu.cn

研究方向:数值代数及其应用。

教育和工作经历:

2020.11 – 至今,海南师范大学,数学与统计学院,副教授

2014.05 – 2020.10,兰州大学,数学与统计学院,副教授

2016.08 – 2016.10,中国科学院数学与系统科学研究院,计算数学与科学工程计算研究所,访问副教授

2010.07 – 2011.06,新加坡国立大学,工程院,研究员

2008.07 – 2014.04,兰州大学,数学与统计学院,讲师

2007.02 – 2008.01,浙江大学,理学院,访问学习

2003.09 – 2008.06,兰州大学,数学与统计学院,硕博连读,获博士学位

1999.09 – 2003.06,西北师范大学,数学与应用数学,本科

讲授课程:

本科生:高等代数、常微分方程、偏微分方程、数值分析、微分方程数值解、高等数学、线性代数、信息论基础、离散数学

研究生:有限元方法、非线性问题的牛顿法、稀疏矩阵迭代方法

承担的主要科研项目:

1. 主持国家自然科学基金地区基金(一类大规模稀疏奇异鞍点问题的高效求解算法及预处理技术研究 ,12161030),2022.01—2025.12;

2. 主持国家自然科学基金青年基金(一类大规模稀疏奇异鞍点问题的高效求解算法及预处理技术研究 ,11401281),2015.01—2017.12;

3. 主持国家自然科学基金数学天元基金(增量未知元方法的若干理论与数值分析,11026064),2011.01—2011.12;

4. 主持海南省自然科学基金高层次人才项目(多参数维数分解预处理子及其在电磁场数值模拟中的应用,121RC537),2021.09—2024.06;

5. 作为骨干成员参加国家重点研发计划(高寒内陆盆底水循环全过程高效利用与生态保护技术,2018YFC0406600),2019.01—2021.12;

第一或通讯作者 SCI 论文:

[28]  *Ai-Li Yang, Xue-Qi Chen. The partially greedy randomized extended Gauss-Seidel method for solving the large linear systems. East Asian Journal on Applied Mathematics (2022) Accepted.

[27]  Shi-Ping Tang, *Ai-Li Yang. Banded M-matrix splitting preconditioner for Riesz space fractional reaction-dispersion equation. Journal of Computational Mathematics (2022) Accepted.

[26]  Jun-Li Zhu, Yu-Jiang Wu, *Ai-Li Yang. A two-parameter block triangular preconditioner for double saddle point problem arising from liquid crystal directors modeling. Numerical  Algorithms 89 (2022), no. 3, 987–1006.

[25]  Jun-Li Zhu, *Ai-Li Yang, Yu-Jiang Wu. A parameterized deteriorated PSS preconditioner and its optimization for nonsymmetric saddle point problems,  Computers and Mathematics with Applications 79 (2020) 1420--1434

[24]  Yue Hao, *Ai-Li Yang, Yu-Jiang Wu, How to compute the minimum norm least squares solution of singular linear system by using the preconditioned HSS method? Numerical Algorithms 83(2020) 1205-1221

[23]  *Ai-Li Yang. On the convergence of the minimum residual HSS iteration method, Applied Mathematics Letters, 94(2019)  210--216

[22]  *Ai-Li Yang, Yang Cao, Yu-Jiang Wu. Minimum residual Hermitian and skew-Hermitian splitting iteration methods for non-Hermitian positive definite linear systems, BIT Numerical Mathematics, 59(2019) 299--319

[21]  Yue Hao, *Ai-Li Yang, *Yu-Jiang Wu, How to compute the optimal parameters of the parameterized PMHSS preconditioner? Applied Mathematics Letters, 86 (2018)  8--13

[20]  *Ai-Li Yang, Scaled norm minimization method for computing the parameters of the HSS and the two-parameter HSS preconditioners, Numerical Linear Algebra with Applications,25 (2018) e2169 

[19]  Sheng-Wei Zhou, *Ai-Li Yang, Yu-Jiang Wu. A relaxed block-triangular splitting preconditioner for generalized saddle-point problems. International Journal of Computer Mathematics, 94(2017) 1609--1623

[18]  Yan Dou, *Ai-Li Yang, Yu-Jiang Wu. Modified parameterized inexact Uzawa method for singular saddle-point problems. Numerical Algorithms, 72 (2016) 325--339.

[17]  Sheng-Wei Zhou, *Ai-Li Yang, Yan Dou, Yu-Jiang Wu. The modified shift-splitting preconditioners for nonsymmetric saddle-point problems. Applied Mathematics Letters, 59 (2016) 109--114. 

[16]  *Ai-Li Yang, Yan Dou, Yu-Jiang Wu and Xu Li. On generalized parameterized inexact Uzawa methods for singular saddle-point problems. Numerical Algorithms, 69 (2015) 579--593. 

[15]  *Ai-Li Yang, Yu-Jiang Wu, Zheng-Da Huang and Jin-Yun Yuan. Preconditioning analysis of nonuniform incremental unknowns method for two dimensional elliptic problems. Applied Mathematical Modelling, 39 (2015) 5436--5451.                             

[14]  *Ai-Li Yang, Guo-Feng Zhang and Yu-Jiang Wu. General constraint preconditioning iteration method for singular saddle-point problems. Journal of Computational and Applied Mathematics,  282 (2015) 157--166. 

[13]  *Ai-Li Yang, Xu Li and Yu-Jiang Wu. On semi-convergence of the Uzawa--HSS method for singular saddle-point problems. Applied Mathematics and Computation, 252 (2015) 88--98. 

[12]  Wei-Hong Zhang, *Ai-Li Yang, Yu-Jiang Wu. Parameterized preconditioned Hermitian and skew-Hermitian splitting iteration method for a class of linear matrix equations. Computers & Mathematics with Applications, 70 (2015) 1357--1367.

[11]  *Ai-Li Yang and Yu-Jiang Wu. The Uzawa--HSS method for saddle-point problems. Applied Mathematics Letters, 38 (2014) 38--42.

[10]  *Ai-Li Yang, Yu-Jiang Wu and Zhen-Jian Xu. The semi-convergence properties of MHSS method for a class of complex nonsymmetric singular linear systems. Numerical Algorithms, 66 (2014) 705--719.

[9]   *Ai-Li Yang and Yu-Jiang Wu. Preconditioning analysis of the one dimensional incremental unknowns method on nonuniform meshes. Journal of Applied Mathematics and Computing, 44 (2014) 379--395. 

[8]   Xu Li, *Ai-Li Yang and Yu-Jiang Wu. Lopsided PMHSS iteration method for a class of complex symmetric linear systems. Numerical Algorithms, 66 (2014) 555--568. 

[7]   Yan Dou, *Ai-Li Yang and Yu-Jiang Wu. On semi-convergence of generalized skew-Hermitian triangular splitting iteration methods for singular saddle-point problems. Linear Algebra and its Applications, 459 (2014) 493--510.       

[6]   Xu Li, *Ai-Li Yang and Yu-Jiang Wu. Parameterized preconditioned Hermitian and skew-Hermitian splitting iteration method for saddle-point problems. International Journal of Computer Mathematics, 91 (2014) 1224--1238.       

[5]   *Ai-Li Yang, Lun-Ji Song and Yu-Jiang Wu. Algebraic preconditioning analysis of the multilevel block incremental unknowns method for anisotropic elliptic operators. Mathematical and Computer Modelling, 57 (2013) 512--524.

[4]   *Ai-Li Yang, Yu-Jiang Wu, Yong-Qing Wu and Da-Wei Ren. Bi-parameter incremental unknowns ADI iterative methods for elliptic problems. Numerical Algorithms, 60 (2012), 483--499.

[3]   *Ai-Li Yang and *Yu-Jiang Wu. Newton-MHSS methods for solving systems of nonlinear equations with complex symmetric Jacobian matrices. Numerical Algebra, Control and Optimization, 2(4) (2012), 839--853.

[2]   Li-Nan Sun, Yu-Jiang Wu, *Ai-Li Yang, Uniform convergence analysis of finite difference approximations for advection-reaction-diffusion problem on adaptive grids, International Journal of Computer Mathematics, 88 (2011), 3292-3307.

[1]   Ai-Li Yang, Jing An, Yu-Jiang Wu. A generalized preconditioned HSS method for non-Hermitian positive definite linear systems. Applied Mathematics and Computation, 216 (2010) 1715-1722.