【系综合学术报告】2023年第7期 || Dual Quaternions and Augmented Quaternions (第一场)& Transformed low tubal-rank approximations of third order tensors via frequent directions(第二场)
发布日期:2023/04/19
【系综合学术报告】
1)报告题目:Dual Quaternions and Augmented Quaternions
报告人: 祁力群 教授(香港理工大学、杭州电子科技大学)
时间:2023年4月20日(周四)下午3:00-4:00
报告摘要:In this talk, I will first report our work on eigenvalues of Hermitian dual quaternion matrices. This work extends the classical theory of eigenvalues of Hermitian complex matrices and Zhang's 1997 result on eigenvalues of Hermitian quaternion matrices. Then we apply this result to the formation control study, while formation control is very important in the UAV research. Then I will report our work on augmented quaternions, and formulate hand-eye calibration, which is a basic problem in robotic research, and SLAM (Simultaneous Location and Mapping), which is a very hot topic in robotic research, as equality constrained augmented dual quaternion optimization problems. This approach reduces the size of the problem and keep the smoothness of the model. We explore these two directions from two different points of view to quaternions and dual quaternions. In this talk, I will explain these two different points of view.
报告人简介:祁力群教授,1968年在正规靠谱的网投平台计算数学專业毕业,1981年和1984年在美国威斯康星大学麦迪逊分校计算机科学分别取得硕士学位和博士学位。祁力群教授曾任教于正规靠谱的网投平台,澳大利亚新南威尔士大学,香港城市大学和香港理工大学,现为香港理工大学应用数学榮休教授, 杭州电子科技大学教授。祁力群教授在国际杂志上发表了380多篇论文,在十个囯际杂志担任主编或编委。他建立了半光滑牛顿方法的超线性收敛理论,和光滑化牛顿方法的全局收敛理论,于2010年取得中囯运筹学会科学技术一等奖。祁力群教授的论文在世界上被广泛应用,在2003-2010年度被列为世界髙被引数学家,在2018,2019,2020, 2021 和2022年被再次列为世界髙被引数学家。祁力群教授在2005年提出髙階张量特征值,並继而形成髙階张量谱理论,在医疗工程,数据分析,量子物理,超图谱理论,液晶研究等方面取得应用,並于2017年和2018年分別在美国工业应用数学协会和斯普林格出版社出版张量理论的專著。
2)报告题目:Transformed low tubal-rank approximations of third order tensors via frequent directions
时间:2023年4月20日(周四)下午4:00-5:00
报告摘要:Tensor low rank approximation is an important tool in tensor data analysis and processing. In the sense of T-product derived from general invertible transformation, the best low tubal rank approximation of third order tensors can be obtained through truncated T-SVD. In this talk, we first present two deterministic frequent directions type algorithms for near optimal low tubal rank approximations of third order tensors. Moreover, by combining the fast frequent directions type algorithm with the so-called random count sketch sparse embedding
method, we propose a randomized frequent directions algorithm for near optimal low tubal rank approximations of third order tensors. Corresponding relative error bounds for the presented algorithms are proposed. The related numerical examples on third order tensors of color image, grayscale video and synthetic data with larger scale illustrate the favorable performance of the presented methods compared to some existing methods.
报告人简介:凌晨 , 杭州电子科技大学理学院教授,博士生导师。现任中国运筹学会数学规划分会副理事长、中国经济数学与管理数学研究会副理事长,曾任中国运筹学会理事、中国系统工程学会理事、浙江省数学会常务理事。近十年来,主持国家自科基金和浙江省自科基金各4项、其中省基金重点项目1项。 在Math. Program.、SIAM J. on Optim.、SIAM J.on Matrix Anal.and Appl. 、COAP、JOTA、JOGO等国内外重要刊物发表论文多篇。
邀请人:张立平