報 告 人：江兆林 教授
報告題目：Analytical potential formulae and fast algorithm for a horn torus-resistor network
報告時間：2023年10月17日（周二）上午10:00—11:00
報告地點：靜遠樓204學術報告廳
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：
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、博士和碩士研究生導師，曾任外國語學院院長、國際合作處處長、國際交流學院院長，理學院院長，數學與統計學院黨委書記、院長。山東省中青年學術骨干，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。已在 Physical Review E(美國物理學會會刊)、Sci China Math(中國科學)、Applied Mathematics and Computation、Linear Algebra and its Applications、Journal of Computational Mathematics、Scientific Reports（英國自然子刊）、IET Signal Processing等60余種國內外學術期刊發表學術論文160余篇，其中SCI 檢索65篇，EI 檢索31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。先后主持或參與了國家級、省級等課題19項。先后出訪過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、臺灣大學、香港中文大學、香港理工大學、莫斯科大學、圣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、數值線代數等方面的研究工作。
報告摘要：
Resistor network is widely used. Many potential formulae of resistor networks have been solved accurately, but the scale of data is limited by manual calculation, and numerical simulation has become the trend of large-scale operation. In this talk, a horn torus resistor network with an arbitrary boundary is researched. According to the modified Recursion-Transform method (RT-V), we obtain the general solution potential formula between two points on any axis. Firstly, the recursive matrix equation model is established by a perturbed tridiagonal Toeplitz matrix, and then the orthogonal matrix transformation is constructed to obtain the eigenvalues and eigenvectors of this perturbed tridiagonal Toeplitz matrix; Secondly, the boundary condition constraint equation model is established; Finally, the solution of the node voltage is given by using the inverse matrix transformation. We introduce Chebyshev polynomials to represent the general solution of the resistor network. In addition, a fast algorithm for solving matrix equations is proposed by using the famous fifth type of discrete sine transform. In the application of the formula, the equivalent resistance formulae in special cases are given and displayed by a three-dimensional dynamic view. The potential formula and the proposed fast algorithm realize large-scale operation.