講座主題：Explicit potential function and fast algorithm for computing potentials in α×β conic surface resistor network
專(zhuān)家姓名：江兆林
工作單位：臨沂大學(xué)
講座時(shí)間：2024年05月27日09:00-11:00
講座地點(diǎn)：數(shù)學(xué)與信息科學(xué)學(xué)院341大會(huì)議室
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)容摘要：
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.
主講人介紹：
江兆林，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(shū)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(shū)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、Expert Systems with Applications、Sci China Math(中國(guó)科學(xué))、Applied Mathematics and Computation、Linear Algebra and its Applications、Journal of Computational Mathematics、Scientific Reports、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(zhuān)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(lèi)讀物8部。先后主持或參與了國(guó)家級(jí)、省級(jí)課題等19項(xiàng)。先后出訪過(guò)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）。
主要從事圖像處理、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。
