江蘇省應用數學（中國礦業大學）中心系列學術報告
報告題目：Explicit potential function and fast algorithm for computing potentials in α×β conic surface resistor network
時 間：2023年10月 16 日（星期 一 ），下午 3：30-4：30
地 點：中國礦業大學應用數學中心（伟德bvA321）
主 辦：中國礦業大學伟德bv
參加對象：感興趣的老師和研究生
報告摘要：Resistor network research is of great importance, yet many resistor networks and their large-scale fast computations have not received sufficient attention. This talk proposes a new resistor network with idiosyncratic shape, i.e., a α× β conic surface resistor network that resembles the upper part of a three-dimensional Dirac function. Utilizing the Recursion Transform (RT-V) method, a recursive matrix equation model is constructed based on Kirchhoff’s law and nodal voltages, which contains the modified tridiagonal Toeplitz matrix. By using the orthogonal matrix transformation, the eigenvalues and eigenvectors of the modified tridiagonal Toeplitz are obtained. The discrete sine transform of the fourth type (DST-IV) is utilized to solve node voltages, while the explicit potential function is represented by the Chebyshev polynomials of the second kind. In addition, explicit potential functions for some special cases are provided, and the potential distribution is illustrated using dynamic three-dimensional graph. To achieve a rapid calculation of the potential, a fast algorithm based on the multiplication of DST-IV with a vector is proposed. In the end, analysis of computational efficiency for the explicit potential function and the fast algorithm are shown.
報告人簡介：江兆林，現任臨沂大學數學與科學計算研究所所長，校特聘二級教授、首批沂蒙學者特聘教授、博士生導師，曾任理學院院長、數學與統計學院院長等。山東省中青年學術骨幹，山東省首屆教指委成員、美國數學會評論員、中國線性代數學會副秘書長、中國運籌學會線性規劃分會理事。在 Physical Review E、Sci China Math、Applied Mathematics and Computation、Linear Algebra and its Applications、Journal of Computational Mathematics、Scientific Reports、IET Signal Processing等60餘種國内外學術期刊發表學術論文160餘篇，其中SCI檢索65篇。出版專著一部，主編、主審高校教材10多部, 主編、主審數學教育類讀物8部。先後主持或參與了國家級、省級等課題19項。先後出訪過10個國家（地區）的60多所大學（如：牛津大學、劍橋大學、哈佛大學、斯坦福大學、東京大學、名古屋大學、洪堡大學、巴黎高師、首爾大學、台灣大學、香港中文大學、香港理工大學、莫斯科大學、聖彼得堡國立技術大學等）。主要從事圖象處理、電阻網絡、神經網絡、機器人路徑規劃、特殊矩陣的理論、算法及其應用、數值代數等方面的研究工作。