應(yīng)yl7703永利官網(wǎng)鄭兵教授的邀請，清華大學(xué)數(shù)學(xué)科學(xué)系賈仲孝教授將于2019年11月15日至11月17日訪問我校并作學(xué)術(shù)報告。

報告題目I：The Convergence of the Generalized Lanczos Trust-Region Method for the Trust-Region Subproblem

時間：2019年11月15日(星期五)晚上19:30

地點：觀云樓610教室

摘要：Solving the trust-region subproblem (TRS) plays a key role in numerical optimization and many other applications. The generalized Lanczos trust-region (GLTR) method is a well-known Lanczos type approach for solving a large-scale TRS. The method projects the original large-scale TRS onto a dimensional Krylov subspace, whose orthonormal basis is generated by the symmetric Lanczos process, and computes an approximate solution from the underlying subspace. There have been some a-priori error bounds for the optimal solution and the optimal objective value in the literature, but no a-priori result exists on the convergence of Lagrangian multipliers involved in projected TRS's and the residual norm of approximate solution. In this paper, a general convergence theory of the GLTR method is established, and a-priori bounds are derived for the errors of the optimal Lagrangian multiplier, the optimal solution, the optimal objective value and the residual norm of approximate solution. Numerical experiments demonstrate that our bounds are realistic and predict the convergence rates of the three errors and residual norms accurately.

報告題目II：On choices of formulations of computing the generalized singular value decomposition of a matrix pair

時間：2019年11月16日(星期六)上午9:00

地點：齊云樓911報告廳

摘要：For the computation of the generalized singular value decomposition(GSVD) of a matrix pair

of full column rank, the GSVD is commonly formulated as two mathematically equivalent generalized eigenvalue problems, so that a generalized eigensolver can be applied to one of them and the desired GSVD components are then recovered from the computed generalized eigenpairs. Our concern in this paper is, in finite precision arithmetic, which formulation of the generalized eigenvalue problems is numerically preferable to compute the desired GSVD components more accurately. A detailed perturbation analysis is made on the two formulations and shows how to make a suitable choice between them. Numerical experiments illustrate the obtained results.

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報告人簡介

賈仲孝，清華大學(xué)數(shù)學(xué)科學(xué)系二級教授、博士生導(dǎo)師。曾任中國工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(CSIAM)常務(wù)理事，中國計算數(shù)學(xué)學(xué)會常務(wù)理事；現(xiàn)任北京數(shù)學(xué)會副理事長，清華大學(xué)數(shù)學(xué)科學(xué)系學(xué)術(shù)委員會副主任。1994年于德國Bielefeld大學(xué)獲得理學(xué)博士學(xué)位，長期從事數(shù)值線性代數(shù)、矩陣計算、科學(xué)計算等研究領(lǐng)域。在矩陣特征值問題、奇異值分解問題的數(shù)值解法的理論和算法領(lǐng)域做出了系統(tǒng)的、有重要國際影響的研究成果，在國際學(xué)術(shù)界引發(fā)了大量的后續(xù)研究。1993年在牛津大學(xué)被英國“數(shù)學(xué)及其應(yīng)用學(xué)會(IMA)”授予“第六屆國際青年數(shù)值分析家獎-Leslie Fox獎”；入選1999度“國家百千萬人工程”；1999年國務(wù)院政府專家特殊津貼稱號；2000年兩篇論文被美國科學(xué)信息所（ISI）授予在國際上有高影響力論文（High Impact Papers）的“經(jīng)典引文(Citation Classic Award)”；2001年清華大學(xué)“百人計劃”特聘教授。迄今為止在Math. Comput., Numer. Math., SIAM J. Sci. Comput., SIAM J. Matrix Anal. Appl.等國際頂尖和著名雜志上發(fā)表論文60篇，研究成果被36個國家和地區(qū)的600多名專家與研究人員在14部經(jīng)典著作、專著、教材及近600篇論文中引用逾1000篇次。

甘肅省應(yīng)用數(shù)學(xué)與復(fù)雜系統(tǒng)重點實驗室

yl7703永利官網(wǎng)

萃英學(xué)院

2019年10月13日