应兰州大学数学与统计学院郑兵教授的邀请，清华大学数学科学系贾仲孝教授将于2019年11月15日至11月17日访问我校并作学术报告。

报告题目I：The Convergence of the Generalized Lanczos Trust-Region Method for the Trust-Region Subproblem

时间：2019年11月15日(星期五)晚上19:30

地点：观云楼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.

报告题目II：On choices of formulations of computing the generalized singular value decomposition of a matrix pair

时间：2019年11月16日(星期六)上午9:00

地点：齐云楼911报告厅

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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报告人简介

贾仲孝，清华大学数学科学系二级教授、博士生导师。曾任中国工业与应用数学学会(CSIAM)常务理事，中国计算数学学会常务理事；现任北京数学会副理事长，清华大学数学科学系学术委员会副主任。1994年于德国Bielefeld大学获得理学博士学位，长期从事数值线性代数、矩阵计算、科学计算等研究领域。在矩阵特征值问题、奇异值分解问题的数值解法的理论和算法领域做出了系统的、有重要国际影响的研究成果，在国际学术界引发了大量的后续研究。1993年在牛津大学被英国“数学及其应用学会(IMA)”授予“第六届国际青年数值分析家奖-Leslie Fox奖”；入选1999度“国家百千万人工程”；1999年国务院政府专家特殊津贴称号；2000年两篇论文被美国科学信息所（ISI）授予在国际上有高影响力论文（High Impact Papers）的“经典引文(Citation Classic Award)”；2001年清华大学“百人计划”特聘教授。迄今为止在Math. Comput., Numer. Math., SIAM J. Sci. Comput., SIAM J. Matrix Anal. Appl.等国际顶尖和著名杂志上发表论文60篇，研究成果被36个国家和地区的600多名专家与研究人员在14部经典著作、专著、教材及近600篇论文中引用逾1000篇次。

甘肃省应用数学与复杂系统重点实验室

数学与统计学院

萃英学院

2019年10月13日