题目：Explicit potential function and fast algorithm for computing potentials in α×β conic surface resistor network

主讲人：江兆林

讲座时间：11月21日（周二）15:00-16:00
地点：综合楼644会议室
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，数学与太阳集团电子游戏党委书记、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)、Expert Systems with Applications、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、省级课题等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 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.