报告人：黄荣 教授
报告题目：Threshold-Free Eaxct Rank Decay and Accurate Nested Range Subspace Tracking for Rank-Deficient Matrix Powers
报告时间：2025年12月20日（周六）下午4：00
报告地点：云龙校区6号楼304报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
黄荣，教授、博士生导师、湖南省杰出青年基金获得者、湖南省芙蓉学者奖励计划获得者、湖南省普通高校学科带头人、湖南省新世纪121人才工程人选、湖南省普通高校青年骨干教师。主要从事数值计算方面的研究工作，已（独立）主持获得2022-2023年度湖南省自然科学奖二等奖1项，以及主持获得湖南省高等教育教学成果奖二等奖1项，担任国际学术期刊《Numerical Algebra, Control and Optimization》编委等，已主持国家自然科学基金面上项目、国家自然科学基金青年项目、教育部博士点基金、湖南省杰出青年科学基金、中国博士后基金、湖南省教育厅重点项目、湖南省科技计划项目等，研究成果全部以独著或第一作者方式发表在Math. Comp.、SIAM. J. Matrix Anal. Appl.、J. Sci. Comput.、Adv. Comp. Math.、Appl. Numer. Math.、BIT、Numer. Linear Algebra Appl.等。
报告摘要：
This talk presents a threshold-free LU iteration method that employs Neville-type representations (NRs) to compute the generalized null space decomposition (GNSD). At each LU iteration step, the NR parametrization is updated via specialized updating/downdating algorithms with adaptive rank adjustments. One advantage of our approach is its avoidance of numerical thresholds and its reliance on subtraction-free arithmetic operations. This guarantees exact determination of the rank decay and stabilization index, and accurate computations of nested range subspaces. Consequently, the complete GNSD structure is accurately recovered: (i) the basis transformation matrices are accumulated in a subtraction-free manner, (ii) all zero Jordan blocks are exactly identified, and (iii) all nonzero eigenvalues are computed to high relative accuracy. Numerical experiments validate the high relative accuracy of our proposed method in handling structured and rank-deficient matrices, where conventional threshold-based schemes fail.
