报告人：郑重

报告题目：On Euler-extrapoated double-step scale splitting method for a class of complex symmetric linear systems

时间：12月11日（周六）下午2：00

地点：理工楼631

报告摘要：We propose an Euler-extrapolated double-step scale splitting (EDSS) iteration method for solving a class of complex symmetric linear systems. Under appropriate constraints, we prove that the EDSS method is unconditionally convergent. Furthermore, we illustrate that the spectral radius of the EDSS iteration matrix does not exceed 0.41057 when the argumentθis2π/45and the relaxation parameterαis 0.27614 or 3.62132, respectively. Numerical experiments verify the correctness of the theoretical results and demonstrate the effectiveness of the EDSS method.

报告人简介

郑重，博士，硕士生导师。主要从事数值代数及微分方程的数值算法研究。以第一作者在Applied Mathematics Letters、Journal of Computational and Applied Mathematics、BIT Numerical Mathematics、Journal of Computational Mathematics等期刊上发表论文10余篇。现主持国家自然科学基金青年基金1项，河南省高等学校重点科研项目1项。2017年获河南省第四届本科高校青年教师技能竞赛一等奖。

报告人：廖丽丹

时间：12月11日（周六）下午3：00

地点：理工楼631

题目：Preconditioned iterative method for nonsymmetric saddle point linear systems

报告摘要：In this paper, a new preconditioned iterative method is presented to solve a class of nonsymmetric nonsingular or singular saddle point problems. The implementation of the proposed preconditioned Krylov subspace method avoids solving inverse of Schur complement and only needs to solve one linear sub-system at each step, which implies that it may save considerable costs. Theoretical convergence analysis, including the bounds of eigenvalues and eigenvectors, the degree of the minimal polynomial of the preconditioned matrix, are discussed in details. Moreover, a novel algebraic estimation technique for finding a practical iteration parameter is presented, which is very effective and practical even for large scale problems. At last, some numerical examples are carried, showing that the theoretical results are valid and convincing.

报告人简介

廖丽丹，博士。南昌大学赣江青年学者。研究方向为偏微分方程数值问题及图像处理问题中的高效数值代数算法研究。主持国家级和省部级科研项目各一项，获批2020年国家留学基金委面上项目资助，参与国家级项目多项，完成中央高校优秀研究生创新项目一项，发表SCI论文多篇，参编国家级教材2部。获南昌大学理学院“十佳教书育人奖”，省级一流课程建设主要参与人。

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2021年12月10日