應(yīng)yl7703永利官網(wǎng)張國鳳教授和梁兆正博士邀請，南京航空航天大學(xué)戴華教授，上海交通大學(xué)王增琦副教授將于2021年5月2日在線舉辦專題學(xué)術(shù)報(bào)告。
題目：Regularized Least Squares Methods for Locality Preserving Projection
時(shí)間：2021年5月2日（星期日）10：30
騰訊會(huì)議ID：303 625 584
報(bào)告摘要：Locality preserving projection (LPP), as a well-known technique for dimensionality reduction,is designed to preserve the local structure of the original samples which usually lieon a low-dimensional manifold in the real world. However, it suffers from the undersampledor small-sample-size problem, when the dimension of the features is larger than the numberof samples which causes the corresponding generalized eigenvalue problem to be ill-posed.To address this problem, in this talk we show that LPP is equivalent to a multivariate linearregression under a mild condition, and establish the connection between LPP and a LS problemwith multiple columns on the right-hand side. Based on the developed connection, wepropose two regularized least squares methods for solving LPP and discuss the applicationof these methods to image recognition.
報(bào)告人簡介：戴華，1988年畢業(yè)于南京大學(xué)數(shù)學(xué)系計(jì)算數(shù)學(xué)專業(yè)，獲博士學(xué)位?，F(xiàn)任南京航空航天大學(xué)理學(xué)院教授、博士生導(dǎo)師。擔(dān)任《高等學(xué)校計(jì)算數(shù)學(xué)學(xué)報(bào)》副主編、《Numerical Algebra, Control and Optimization》等刊物編委。長期從事數(shù)值代數(shù)、動(dòng)力學(xué)反問題等方向的研究，先后承擔(dān)了國家自然科學(xué)基金、江蘇省自然科學(xué)基金等項(xiàng)目10多項(xiàng)，在大型線性方程組數(shù)值方法、矩陣特征值問題及其靈敏度分析、代數(shù)特征值反問題的理論與方法、矩陣方程與矩陣逼近及其在結(jié)構(gòu)模型修正中的應(yīng)用等方面取得了一系列研究成果，在國內(nèi)外重要學(xué)術(shù)刊物上發(fā)表論文180余篇，出版著作《代數(shù)特征值反問題》和《矩陣論》。曾獲江蘇省科技進(jìn)步獎(jiǎng)一項(xiàng)。長期從事大學(xué)數(shù)學(xué)的教學(xué)，先后為本科生、碩士生和博士生講授不同的數(shù)學(xué)課程20多門。先后承擔(dān)多項(xiàng)教改項(xiàng)目，是國家雙語教學(xué)示范課程“線性代數(shù)”和江蘇省優(yōu)秀研究生課程“矩陣論”的負(fù)責(zé)人，曾獲江蘇省教學(xué)成果一等獎(jiǎng)。曾獲霍英東教育基金會(huì)高等學(xué)校優(yōu)秀青年教師獎(jiǎng)、江蘇省“紅杉樹”園丁獎(jiǎng)，被評為江蘇省高校教學(xué)名師、全國優(yōu)秀教師，享受政府特殊津貼。
題目：Application of Splitting Preconditioners to the Fluid Flow Control Problems
時(shí)間：2021年5月2日（星期日）11：30
騰訊會(huì)議ID：303 625 584
報(bào)告摘要：Fluid flow control problems play an important role in industrial scientific applications.The optimal control of the Navier-Stokes equations is the most attractive one. On the basis of effective preconditioning for the Poisson control and Stoke control problems, we study the preconditioners for solving the Navier-Stokes control problem. Linearized by Picard’s iterations, Navier-Stokes control problem yields a sequence of large sparse structured linear systems. The coefficient matrices are in the two-by-two block form with square blocks. We take advantage of the block structure to exploit the preconditioners. The eigenvalue distribution of the achieved preconditioned matrix is illustrated by the norms of the submatrices. To avoid solving the saddle point subsystems in the preconditioning procedure, we propose a practical variant of the preconditioner. The numerical experiments show that the GMRES method with the proposed preconditioners is the efficient and effective solution for the Picard’s iterations with the variable viscosity coefficient. The iteration count of the preconditioned method is independent of mesh size and the regularization parameter.
報(bào)告人簡介：王增琦，中國科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院計(jì)算數(shù)學(xué)與科學(xué)工程計(jì)算研究所博士，上海交通大學(xué)數(shù)學(xué)科學(xué)學(xué)院副教授。2007.7畢業(yè)于中國科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院計(jì)算數(shù)學(xué)與科學(xué)工程計(jì)算研究所，獲博士學(xué)位。2007年到上海交通大學(xué)數(shù)學(xué)系工作，2011年晉升為副教授。先后獲得上海交通大學(xué)晨興青年教師獎(jiǎng)C類與上海交通大學(xué)SMC青年教師獎(jiǎng)B類。主要研究領(lǐng)域?yàn)閿?shù)值線性代數(shù)，結(jié)構(gòu)化大型系數(shù)方程組的迭代算法，預(yù)處理技術(shù)，最小二乘問題的數(shù)值求解。曾到日本國立情報(bào)學(xué)研究所及美國加州大學(xué)伯克利分校做訪問學(xué)者。曾先后主持國家自然科學(xué)基金2項(xiàng)，發(fā)表論文十余篇。曾組織The Seventh China-Russia Conference on Numerical Algebra with Applications、Forum on frontiers of numerical algebra at Shanghai Jiao Tong University等學(xué)術(shù)會(huì)議。
甘肅省高校應(yīng)用數(shù)學(xué)與復(fù)雜系統(tǒng)重點(diǎn)實(shí)驗(yàn)室
yl7703永利官網(wǎng)
萃英學(xué)院
2021年4月30日
