Series of Academic Reports of Jiangsu Applied Mathematics (China University of Mining and Technology) Center

Report Title: The Wasserstein Metric Matrix and Its Computational Property

Presenter: Researcher Bai Zhongzhi, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Report Time: 10:00-11:00 a.m. on Thursday, May 15, 2025

Report Location: Room A321, School of Mathematics

Speaker Profile: Bai Zhongzhi is a researcher and doctoral supervisor at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and an honorary doctor of the Southern Federal University of Russia. He has received the National Science Fund for Distinguished Young Scholars, the Feng Kang Scientific Computing Award, and the Special Government Allowance of The State Council, etc. He has also been selected into the National "New Century Hundred, Thousand and Ten Thousand Talents Project" and the "Hundred Talents Program of the Chinese Academy of Sciences" (Category D, i.e., domestic category). He has been invited many times to give keynote invitation speeches at important international conferences. He/She has served as the co-chair of many important international conferences and a member of the organizing committee or scientific committee on multiple occasions. He/She has also served or is currently serving as an editorial board member of at least fifteen international and domestic academic journals. Researcher Bai Zhongzhi's main research fields include numerical algebra, numerical optimization, parallel computing, and numerical solutions of differential equations, etc. He designed efficient serial and parallel iterative methods for the numerical solutions of linear and nonlinear algebraic equations, algebraic Riccati equations, algebraic eigenvalue problems, discrete complementarity problems, discrete integers and fractional differential equations, and established a profound convergence theory of the system. Researcher Bai Zhongzhi has consistently ranked among the top in Elsevier's list of highly cited Chinese researchers for many consecutive times, and has been included in the list of highly cited global researchers by Thomson Reuters ISI Web of Science for five consecutive times from 2016 to 2020. In particular, the HSS iterative method proposed by him in 2003 along with Gene H. Golub, an academician of the National Academy of Sciences, the National Academy of Engineering and the National Academy of Arts of the United States and a professor at Stanford University, is recognized as a milestone in matrix computing and one of the most significant advancements in the field of iterative methods for linear algebraic equations in the past three decades.

Report Summary: By further exploring and deeply analyzingthe concrete algebraic structures andessential computational properties aboutthe Wasserstein-1 metric matrices ofone- and two-dimensions, we show that theycan be essentially expressed by the Neumann seriesof nilpotent matrices and, therefore, the products ofthese matrices with a prescribed vector can be accomplishedaccurately and stably in the optimal computationalcomplexities through solving unit bidiagonal triangularsystems of linear equations. We also give appropriategeneralizations of these one- and two-dimensionalWasserstein-1 metric matrices, as well as theircorresponding extensions to higher dimensions,and demonstrate the algebraic structures andcomputational properties of these generalized andextended Wasserstein-1 metric matrices.