»ã±¨±êÌâ (Title)£ºThe Wasserstein Metric Matrix and Its Computational Property £¨Wasserstein»³±§¾ØÕó¼°ÆäÍÆËã¸öÐÔ£©

»ã±¨ÈË (Speaker)£º°×ÖÐÖÎ ×êÑÐÔ±£¨Öйú¿ÆѧԺÊýѧÓëϵͳ¿Æѧ×êÑÐÔº£©

»ã±¨¹¦·ò (Time)£º2025Äê10ÔÂ23ÈÕ£¨ÖÜËÄ£©14:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿ F309

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»ã±¨ÌáÒª£º 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.