报告题目：A randomized singular value decomposition for third-order oriented tensors

报告人：解朋朋 博士

报告人单位：中国海洋大学数学科学学院

报告时间：2024年10月17日下午2:00-3:00

会议地点：数学科学学院301

主办单位：曲阜师范大学数学科学学院

报告摘要：The oriented singular value decomposition (O-SVD) proposed in [Numer. Linear Algebra Appl., 27(2020), e2290] provides a hybrid approach to the t-product based third-order tensor singular value decomposition with the transform matrix being a factor matrix of the higher order singular value decomposition. Continuing along this vein, this paper explores realizing the O-SVD more efficiently by the tensor-train rank-1 decomposition and gives a truncated O-SVD. Motivated by the success of probabilistic algorithms, we develop a randomized version of the O-SVD and present its detailed error analysis. The new algorithm has advantages in efficiency while keeping good accuracy compared with the current tensor decompositions. Our claims are supported by numerical experiments on several oriented tensors from real applications.

报告人简介：解朋朋，中国海洋大学数学科学学院讲师、硕士生导师。2015年毕业于复旦大学数学科学学院计算数学专业，获理学博士学位。研究领域和兴趣：数值代数、张量计算等。在SIAM J. Matrix Anal. Appl.、 Advances in Computational Mathematics、Applied Mathematics Letters、Numer. Linear Algebra Appl.,、Numer. Algor.、Linear Algebra Appl.等期刊发表论文。主持国家自然科学基金青年基金项目1项，作为主要参与人参与国家自然科学基金面上项目1项。