报告题目：A new complex structure-preserving method for QSVD
时 间：2024年8月26日（星期一）14：30
地 点：腾讯会议（634-381-199）
主 办：数学与统计学院、分析数学及应用教育部重点实验室、福建省分析数学及应用重点实验室、统计学与人工智能福建省高校重点实验室、福建省应用数学中心（福建师范大学）
参加对象：感兴趣的老师和学生
报告摘要：In this paper, we propose a new structure-preserving algorithm for computing the singular value decomposition of a quaternion matrix A. We first define a quaternion-type matrix and prove that the multiplication of two quaternion-type matrices still be a quaternion-type matrix. Thus, utilizing this fact, we conduct a sequence of quaternion-type unitary transformations on a half of the elements of the complex adjoint matrix XA of A instead of on the whole XA. Then, we recover the resulting matrix with the help of the special structures. Compared with direct performing on the complex adjoint matrix, our algorithm needs only half of the computation and storage. This method also provides a novel proof for the existence of the singular value decomposition of a quaternion matrix. Moreover, numerical experiments are given to demonstrate the validity of our approach.
报告人简介：刘新副教授，博士生导师，其一直致力于研究广义四元数及其衍生体上的矩阵、张量理论及其在信号处理中的应用。目前，已在相关领域积累了一些的经验和成果。在Journal of Scientific Computing，Applied Mathematics and Computation 等国内外重要学术刊物与国内外专家合作发表 SCI 学术论文30余篇，与多位线性代数专家合著书籍一部(Springer 出版社)，且主持4项澳门科技发展基金。