2026年10月9日（周五）下午2:30，深圳河套学院荣幸地邀请到湘潭大学数学与计算科学学院副院长张娟教授，在B301教室带来主题为“求解大型稀疏线性系统的混合精度广义交替方向隐式方法”的学术报告分享。诚挚欢迎学院师生及对该领域感兴趣的产学研界同仁参与讲座。

Title

求解大型稀疏线性系统的混合精度广义交替方向隐式方法
Mixed Precision General Alternating-Direction Implicit Method for Solving Large Sparse Linear Systems

About the Speaker

张娟 教授
Prof. Zhang Juan

张娟，教授，博士生导师，湘潭大学数学与计算科学学院副院长，“智能计算与信息处理”教育部重点实验室常务副主任。入选湖湘青年英才，省青年骨干教师培养对象。多次赴新加坡国立大学、澳门大学访问。主持国自科面上、开元国际研究院课题、711研究所项目。作为子课题负责人承担国家重点研发计划、工信部项目。主要从事数值代数、控制理论研究。近5年在计算数学、控制领域、数据科学权威期刊SINUM、SISC、Automatica、IEEE TKDE、JCP、JSC、CSIAM-AM发表学术论文20余篇。

Professor Zhang Juan, serves as Vice Dean of the School of Mathematics and Computational Science, Xiangtan University, and Executive Deputy Director of the Key Laboratory of Intelligent Computing and Information Processing, Ministry of Education. She was selected into the Huxiang Youth Talent Program and the Hunan Provincial Training Program for Young Backbone Teachers. She has been a visiting scholar at the National University of Singapore and the University of Macau on multiple occasions. She presides over the General Program of the National Natural Science Foundation of China, research projects of Kaiyuan International Research Institute, and projects of the 711 Research Institute. As the sub-project principal investigator, she undertakes the National Key R&D Program, projects of the Ministry of Industry and Information Technology. Her main research interests include numerical algebra and control theory. In the past five years, she has published more than 20 academic papers in top journals in computational mathematics, control theory and data science, including SINUM, SISC, Automatica, IEEE TKDE, JCP, JSC and CSIAM-AM.

Abstract

本次报告提出一种全新的广义交替方向隐式（GADI）方法混合精度格式，专门用于加速大规模稀疏线性方程组的求解。该方法在计算量大的子系统上采用低精度（例如Bfloat16或FP32）进行运算，而残量计算与解更新则采用高精度运算。该方案可显著缩短计算耗时，同时不损失最终解的精度。本文开展了完备的舍入误差分析，严格证明了混合精度算术下该方法的收敛速度与极限精度。此外，项目团队提出一种基于高斯过程回归（GPR）的稳健策略，用于正则化参数的最优选取。基于NVIDIA A100 GPU开展性能基准测试，在大规模对流-扩散与反应-扩散问题上进行数值试验；结果表明，相较于标准双精度实现，该混合精度GADI方法最高可实现2.6倍加速。

This talk introduces a novel mixed-precision formulation of the general alternating-direction implicit (GADI) method, specifically designed to accelerate the solution of large-scale sparse linear systems. By computing the computationally intensive subsystems in low precision (e.g., Bfloat16 or FP32) while performing residual calculations and solution updates in high precision, the proposed approach achieves a significant reduction in execution time without sacrificing the final solution accuracy. This paper presents a comprehensive rounding error analysis, which rigorously establishes the convergence rate and limiting accuracy of the method under mixed-precision arithmetic. Furthermore, the project team proposes a robust strategy based on Gaussian process regression (GPR) for the optimal selection of the regularization parameter. Performance benchmarks conducted on an NVIDIA A100 GPU demonstrate that the mixed-precision GADI method delivers speedups of up to 2.6× compared to standard double-precision implementations, with tests performed on large-scale convection-diffusion and reaction-diffusion problems.

Host

陈淙靓 助理教授

Prof. Chen Congliang

Date & Time

2026年10月9日（星期五）

下午2:30-3:30

October 9, 2026, Friday,

2:30pm-3:30pm

Venue

深圳河套学院B301教室

（深圳市福田区福保街道红棉路6号，地图导航“深圳河套学院-南门”）

Room B301, Shenzhen Loop Area Institute

(6 Hongmian Rd, Fubao Sub-Street, Futian District, Shenzhen, navigate to "Shenzhen Loop Area Institute (South Gate)" on the map.)

Online link

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腾讯会议号：948-1135-4043

Tencent Meeting: 948-1135-4043