報告人：林學磊 副教授
報告題目：A fast direct solver for Toeplitz-like Hessenberg systems with application to numerical solution of a fractional diffusion equation
報告時間：2026年5月9日（周六）下午16:00—17:00
報告地點：云龍校區6號樓304報告廳
主辦單位：數學與統計學院、數學研究院、科學技術研究院
報告人簡介：
林學磊，哈爾濱工業大學（深圳）、副教授，主要從事計算機仿真模擬、圖像處理、科學計算，數值線性代數等方面研究。主持國家級、省部級自然科學基金；以第一作者或通訊作者身份發表SCI一區期刊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。曾在世界華人數學家大會上獲得ICCM畢業論文獎-博士論文獎; 獲”第十四屆EASIAM年會“優秀學生論文獎; 獲澳門研究生科技研發獎等多項獎項。研究成果得到國外內同行的廣泛引用和積極評價。擔任多個SCI一區期刊的期刊審稿人，擔任美國數學評論員。
報告摘要：
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.