報(bào)告人：黃榮 教授
報(bào)告題目：Threshold-Free Eaxct Rank Decay and Accurate Nested Range Subspace Tracking for Rank-Deficient Matrix Powers
報(bào)告時(shí)間：2025年12月20日（周六）下午4：00
報(bào)告地點(diǎn)：云龍校區(qū)6號(hào)樓304報(bào)告廳
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院
報(bào)告人簡(jiǎn)介：
黃榮，教授、博士生導(dǎo)師、湖南省杰出青年基金獲得者、湖南省芙蓉學(xué)者獎(jiǎng)勵(lì)計(jì)劃獲得者、湖南省普通高校學(xué)科帶頭人、湖南省新世紀(jì)121人才工程人選、湖南省普通高校青年骨干教師。主要從事數(shù)值計(jì)算方面的研究工作，已（獨(dú)立）主持獲得2022-2023年度湖南省自然科學(xué)獎(jiǎng)二等獎(jiǎng)1項(xiàng)，以及主持獲得湖南省高等教育教學(xué)成果獎(jiǎng)二等獎(jiǎng)1項(xiàng)，擔(dān)任國(guó)際學(xué)術(shù)期刊《Numerical Algebra, Control and Optimization》編委等，已主持國(guó)家自然科學(xué)基金面上項(xiàng)目、國(guó)家自然科學(xué)基金青年項(xiàng)目、教育部博士點(diǎn)基金、湖南省杰出青年科學(xué)基金、中國(guó)博士后基金、湖南省教育廳重點(diǎn)項(xiàng)目、湖南省科技計(jì)劃項(xiàng)目等，研究成果全部以獨(dú)著或第一作者方式發(fā)表在Math. Comp.、SIAM. J. Matrix Anal. Appl.、J. Sci. Comput.、Adv. Comp. Math.、Appl. Numer. Math.、BIT、Numer. Linear Algebra Appl.等。
報(bào)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.