報(bào) 告 人：江兆林 教授
報(bào)告題目：Analytical potential formulae and fast algorithm for a horn torus-resistor network
報(bào)告時(shí)間：2023年10月17日（周二）上午10:00—11:00
報(bào)告地點(diǎn)：靜遠(yuǎn)樓204學(xué)術(shù)報(bào)告廳
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院
報(bào)告人簡(jiǎn)介：
江兆林，現(xiàn)任臨沂大學(xué)數(shù)學(xué)與科學(xué)計(jì)算研究所所長(zhǎng)，校特聘二級(jí)教授、首批沂蒙學(xué)者特聘教授、博士和碩士研究生導(dǎo)師，曾任外國(guó)語(yǔ)學(xué)院院長(zhǎng)、國(guó)際合作處處長(zhǎng)、國(guó)際交流學(xué)院院長(zhǎng)，理學(xué)院院長(zhǎng)，數(shù)學(xué)與統(tǒng)計(jì)學(xué)院黨委書記、院長(zhǎng)。山東省中青年學(xué)術(shù)骨干，山東省首屆教指委成員、美國(guó)數(shù)學(xué)會(huì)評(píng)論員、中國(guó)線性代數(shù)學(xué)會(huì)副秘書長(zhǎng)、中國(guó)運(yùn)籌學(xué)會(huì)線性規(guī)劃分會(huì)理事。已在 Physical Review E(美國(guó)物理學(xué)會(huì)會(huì)刊)、Sci China Math(中國(guó)科學(xué))、Applied Mathematics and Computation、Linear Algebra and its Applications、Journal of Computational Mathematics、Scientific Reports（英國(guó)自然子刊）、IET Signal Processing等60余種國(guó)內(nèi)外學(xué)術(shù)期刊發(fā)表學(xué)術(shù)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(shù)學(xué)教育類讀物8部。先后主持或參與了國(guó)家級(jí)、省級(jí)等課題19項(xiàng)。先后出訪過10個(gè)國(guó)家（地區(qū)）的60多所大學(xué)（如：牛津大學(xué)、劍橋大學(xué)、哈佛大學(xué)、斯坦福大學(xué)、東京大學(xué)、名古屋大學(xué)、洪堡大學(xué)、巴黎高師、首爾大學(xué)、臺(tái)灣大學(xué)、香港中文大學(xué)、香港理工大學(xué)、莫斯科大學(xué)、圣彼得堡國(guó)立技術(shù)大學(xué)等）。主要從事 圖象處理、電阻網(wǎng)絡(luò)、神經(jīng)網(wǎng)絡(luò)、機(jī)器人路徑規(guī)劃、特殊矩陣的理論、算法及其應(yīng)用、數(shù)值線代數(shù)等方面的研究工作。
報(bào)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.