报 告 人：江兆林 教授
报告题目：Analytical potential formulae and fast algorithm for a horn torus-resistor network
报告时间：2023年10月17日（周二）上午10:00—11:00
报告地点：静远楼204学术报告厅
主办单位：太阳集团官方网站入口、数学研究院、科学技术研究院
报告人简介：
江兆林，现任临沂大学数学与科学计算研究所所长，校特聘二级教授、首批沂蒙学者特聘教授、博士和硕士研究生导师，曾任外国语学院院长、国际合作处处长、国际交流学院院长，理学院院长，太阳集团官方网站入口党委书记、院长。山东省中青年学术骨干，山东省首届教指委成员、美国数学会评论员、中国线性代数学会副秘书长、中国运筹学会线性规划分会理事。已在 Physical Review E(美国物理学会会刊)、Sci China Math(中国科学)、Applied Mathematics and Computation、Linear Algebra and its Applications、Journal of Computational Mathematics、Scientific Reports（英国自然子刊）、IET Signal Processing等60余种国内外学术期刊发表学术论文160余篇，其中SCI 检索65篇，EI 检索31篇。 出版专著一部，主编、主审高校教材10多部, 主编、主审数学教育类读物8部。先后主持或参与了国家级、省级等课题19项。先后出访过10个国家（地区）的60多所大学（如：牛津大学、剑桥大学、哈佛大学、斯坦福大学、东京大学、名古屋大学、洪堡大学、巴黎高师、首尔大学、台湾大学、香港中文大学、香港理工大学、莫斯科大学、圣彼得堡国立技术大学等）。主要从事 图象处理、电阻网络、神经网络、机器人路径规划、特殊矩阵的理论、算法及其应用、数值线代数等方面的研究工作。
报告摘要：
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.
