報(bào) 告 人：汪祥 教授

報(bào)告題目：Solving the quadratic eigenvalue problem expressed in non-monomial basis by the tropically scaled CORK linearization

報(bào)告時(shí)間：2023年06月13日（周二）下午15:30—16:30

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：

      汪祥，教授、博士生導(dǎo)師。先后入選或獲批江西省新世紀(jì)百千萬(wàn)人才工程人選，江西省青年科學(xué)家，江西省高等學(xué)校中青年骨干教師，江西省高水平本科教學(xué)團(tuán)隊(duì)負(fù)責(zé)人，江西省優(yōu)秀研究生指導(dǎo)教師，寶鋼全國(guó)優(yōu)秀教師獎(jiǎng)獲得者；擔(dān)任中國(guó)工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)理事，中國(guó)計(jì)算數(shù)學(xué)學(xué)會(huì)理事，中國(guó)高等教育學(xué)會(huì)數(shù)學(xué)專(zhuān)委會(huì)常務(wù)理事, 國(guó)家天元數(shù)學(xué)東南中心執(zhí)委會(huì)委員，國(guó)際知名期刊《Computational and Applied Mathematics》的Associate Editor。

      主要從事數(shù)值代數(shù)、人工智能與數(shù)據(jù)科學(xué)等領(lǐng)域的研究，在大規(guī)模稀疏線(xiàn)性方程組、大規(guī)模稀疏特征值問(wèn)題、線(xiàn)性和非線(xiàn)性矩陣方程的數(shù)值求解、譜聚類(lèi)等方面取得了一些成果。目前主持(含完成)國(guó)家自然科學(xué)基金3項(xiàng)及省部級(jí)項(xiàng)目十幾項(xiàng)。近幾年以第一作者或通訊作者在國(guó)內(nèi)外權(quán)威期刊上共發(fā)表SCI收錄論文50多篇。以第一完成人身份獲江西省自然科學(xué)獎(jiǎng)三等獎(jiǎng)1項(xiàng)和江西省教學(xué)成果獎(jiǎng)二等獎(jiǎng)3項(xiàng)。

報(bào)告摘要：

      In this talk, the quadratic eigenvalue problem (QEP) expressed in various commonly used bases, including Taylor, Newton, and Lagrange basis functions will be introduced. We propose to investigate the backward errors of the computed eigenpairs and condition numbers of eigenvalues incurred by the application of the recently developed and well-received compact rational Krylov (CORK) linearization. To improve the backward error and condition number of QEP expressed in a non-monomial basis, we combine the tropical scaling with the CORK linearization. We then establish upper bounds for the backward error of an approximate eigenpair of the QEP relative to the backward error of an approximate eigenpair of the CORK linearization with and without tropical scaling. Moreover, we get bounds for the normwise condition number of an eigenvalue of the QEP relative to that of the CORK linearization.We unify both bounds and these bounds suggest the tropical scaling to improve the normwise condition number for the CORK linearization and the backward errors of approximate eigenpairs of the QEP obtained from the CORK linearization. Our investigation is accompanied by adequate numerical experiments to justify our theoretical findings.