講座主題：Some Novel Results on Spectral Theory of New-Type Matrices and Applications
專(zhuān)家姓名：張立平
工作單位：清華大學(xué)
講座時(shí)間：2025年11月15日 15:00-16:00
講座地點(diǎn)：二教104
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)容摘要：
In this talk, we mainly introduce some novel results on spectral theory of new-type matrix and application. Testing the positive definiteness of a multivariate form in automatic control is very hard problem. For solving such a problem, M-tensor and strong M-tensor were introduced. Based on the eigenvalue theory of M-tensors, Collatz-type method and smoothing Newton method were proposed, which has the rate of linear convergence and quadratic convergence, respectively. For efficiently handling color video recovery, quaternion tensor was introduced. A novel tensor product for third order quaternion tensors was proposed. With this tensor product, we further defined the singular value decomposition and the rank of a third order quaternion tensor. It was also proved that the best rank-k approximation of a third order quaternion tensor exists, which opens up a new way to analyze the structure of color video. Finally, some experiments are performed to demonstrate the low-rankness of color videos.
主講人介紹：
張立平，清華大學(xué)長(zhǎng)聘教授，博士生導(dǎo)師，研究方向優(yōu)化理論算法及應(yīng)用、機(jī)器學(xué)習(xí)、強(qiáng)化學(xué)習(xí)，在大規(guī)模高維數(shù)據(jù)處理建模、優(yōu)化算法及張量特征值理論等方面取得了重要研究成果。已在JMLR, Math Program, Math Comput, SIAM J Matrix Anal Appl, SIAM J Optim, MOR等優(yōu)化和計(jì)算數(shù)學(xué)國(guó)內(nèi)外核心期刊發(fā)表論文60多篇，連續(xù)獲得多項(xiàng)國(guó)家自然科學(xué)基金面上資助和1項(xiàng)科技部重點(diǎn)研發(fā)專(zhuān)項(xiàng)資助。曾獲得教育部自然科學(xué)獎(jiǎng)二等獎(jiǎng)和北京市科學(xué)技術(shù)獎(jiǎng)二等獎(jiǎng)。
