报告人：林学磊 副教授
报告题目：A fast direct solver for Toeplitz-like Hessenberg systems with application to numerical solution of a fractional diffusion equation
报告时间：2026年5月9日（周六）下午16:00—17:00
报告地点：云龙校区6号楼304报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
林学磊，哈尔滨工业大学（深圳）、副教授，主要从事计算机仿真模拟、图像处理、科学计算，数值线性代数等方面研究。主持国家级、省部级自然科学基金；以第一作者或通讯作者身份发表SCI一区期刊20余篇，包括,SIAM J. Matrix Anal. Appl., SIAM J. Sci. Comput., SIAM J. Numer. Anal., J. Comput. Phys., J. Sci. Comput.等。曾在世界华人数学家大会上获得ICCM毕业论文奖-博士论文奖; 获”第十四届EASIAM年会“优秀学生论文奖; 获澳门研究生科技研发奖等多项奖项。研究成果得到国外内同行的广泛引用和积极评价。担任多个SCI一区期刊的期刊审稿人，担任美国数学评论员。
报告摘要：
In this talk, a novel operator splitting scheme is proposed for a fractional diffusion equation with variable coefficients. By adding perturbation terms, the two-sided diffusion problems are converted into two one-sided sub-problems at each time level. The coefficient matrices of these sub-problems are all non-singular M-matrix and share Toeplitz-like-Hessenberg (TLH) structure, based on which a super fast recursive direct solver is proposed for solving these sub-problems, which requires only $\mathcal{O}(n\log^3n)$ operations and $\mathcal{O}(n)$ storage for an $n\times n$ linear system. As a result, the proposed scheme is fast and directly solvable within a linearithmic complexity in existence of variable coefficients. Theoretically, the unconditional stability, convergence and positivity-preserving property are established for our newly proposed scheme in existence of variable coefficients.