汇报标题 (Title)：The Wasserstein Metric Matrix and Its Computational Property （Wasserstein怀抱矩阵及其推算个性）
汇报人 (Speaker)：白中治 钻研员（中国科学院数学与系统科学钻研院）
汇报功夫 (Time)：2025年10月23日（周四）14:00
汇报地址 (Place)：校本部 F309
约请人(Inviter)：张建军、谭福平
主办部门：理学院数学系
汇报提要： By further exploring and deeply analyzing the concrete algebraic structures and essential computational properties about the Wasserstein-1 metric matrices of one- and two-dimensions, we show that they can be essentially expressed by the Neumann series of nilpotent matrices and, therefore, the products of these matrices with a prescribed vector can be accomplished accurately and stably in the optimal computational complexities through solving unit bidiagonal triangular systems of linear equations. We also give appropriate generalizations of these one- and two-dimensional Wasserstein-1 metric matrices, as well as their corresponding extensions to higher dimensions, and demonstrate the algebraic structures and computational properties of these generalized and extended Wasserstein-1 metric matrices.
