报告题目：高铁二次特征值问题的快速算法

TOPIC:FAST ALGORITHMS FOR FAST TRAIN QUADRATIC EIGENVALUE PROBLEMS

报告时间：2017年5月21日上午10:00

报告地点：数学与统计学院金融实验室

报告人：卢琳璋 教授

报告简介：In the vibration analysis of high speed trains arises such a palindromic quadratic eigenvalue problem (PQEP) (λ2AT + λQ + A)z = 0, where A; Q 2 Cn×n have special structures: both Qand A are m × m block matrices with each block being k × k (thus n = m × k), and Q is complex symmetric and tridiagonal block-Toeplitz, and A has only one nonzero block in the (1; m)th block position which is the same as the subdiagonal block of Q. This PQEP has eigenvalues 0 and 1 each of multiplicity (m − 1)k just by examining A, but it is its remaining 2k eigenvalues, usually nonzero and finite but with an extreme wide range in magnitude, that are of interest. The problem is notoriously difficult numerically. Earlier methods that seek to deflate eigenvalues 0 and 1 first often produce eigenvalues that are too inaccurate to be useful due to the large errors introduced in the deflation process. The solvent approach proposed by Guo and Lin in 2010 changed the situation because it can deliver sufficiently accurate eigenvalues. In this paper, we propose a fast algorithm along the line of the solvent approach. The theoretical foundation of our algorithm is the connection we establish here between this fast train PQEP and a k ×k PQEP defined by the subblocks of A and Q without any computational work. This connection lends itself to a fast algorithm: solve the k × k PQEP and then use its eigenpairs to recover the eigenpairs for the original fast train PQEP. The so-called α-structured backward error analysis that preserves all possible structures in the fast train PQEP to the extreme is studied. Finally numerical examples are presented to show the effectiveness of the new fast algorithm.

专家简介：卢琳璋，厦门大学数学科学学院教授、博导，全国计算数学学会常务理事。1991.6-至今在厦门大学数学系，数学科学学院工作。1992年被评为副教授；1995年被破格评为教授；2001年被评为博士生导师。1995-1996在澳大利亚国立大学和阿德雷德大学访问和工作；1998-1999获得香港CROUCHER基金在香港城市大学访问和工作；2003-2004在香港大学访问和工作;2006在香港浸会访问和工作。1992年至1996年参加过国家科委数学攀登计划项目“大规模科学与工程计算方法和理论”的青年子课题。曾经主持过一项教育部留学回国基金和三项省自然科学基金、两项国家自然科学基金。并作为第一合作者参加物理与机电学院的从2003年开始一项国家自然科学基金“MEMS系统级建模新理论,新方法与仿真研究”(项目号:50275127)。于2002年获得参加973项目第二课题组“物质性质机理的多尺度计算研究”的研究工作.现正参加由中科院余德浩教授主持的一项国家自然科学重点基金“若干非线性问题的数值解法”(项目号:10531080).在国际国内的学术刊物发表了论文40多篇，其中包括在《SIAM J. Matrix Anal. Appl.》、《SIAM J. Scientific Comput.》、《Numer. Linear Algebra Appl.》、《Numerische Mathematik》、《Inverse Problem》、《Linear Algebra Appl.》、《IEEE Trans. Automatic Control》、《IEEE Trans. Information Theory》等10多种SCI,EI国际杂志发表了论文20多篇。其中有多篇论文获得福建省,厦门市优秀论文奖。其独立完成的项目：“两类代数黎卡提方程的数值解法”获得2002年福建省科技进步三等奖。