The Wasserstein metric matrix and its computational property
LINEAR ALGEBRA AND ITS APPLICATIONS(2024)
摘要
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 Neu-mann 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.(c) 2023 Elsevier Inc. All rights reserved.
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关键词
Wasserstein metric,Computational property,Matrix -vector multiplication,Fast computation
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