題目🫅🏽：對偶馬爾科夫鏈與帶非負標準項的對偶數矩陣

演講人：祁力群教授，香港理工大學榮休教授

主持人：林貴華教授🏊🏽，意昂2

時間：2023年10月17日（周二）♐️，下午15:30

地點🛩：意昂2注册校本部東區意昂2官网467室

主辦單位：意昂2、意昂2青年教師聯誼會

演講人簡介👩🏿‍🦳👨‍✈️：

國際知名優化專家，香港理工大學榮休教授🍛，俄羅斯Petrovskaya科學與藝術研究院外籍院士♞，中國運籌學會首屆會士。

中國運籌學會科學技術獎一等獎獲得者，十種國際期刊的主編或編委。

連續多年入選世界高被引科學家，入選 2021 年全球前2%頂尖科學家榜單。

演講內容簡介⛹🏿‍♀️：

We propose a dual Markov chain model to accommodate probabilities as well as perturbation, or error bounds, or variances, in the Markov chain process. This motivates us to extend the Perron-Frobenius theory to dual number matrices with primitive and irreducible nonnegative standard parts. We show that such a dual number matrix always has a positive dual number eigenvalue with a positive dual number eigenvector. The standard part of this positive dual number eigenvalue is larger than or equal to the modulus of the standard part of any other eigenvalue of this dual number matrix. We present an explicit formula to compute the dual part of this positive dual number eigenvalue. The Collatz minimax theorem also holds here. The results are nontrivial as even a positive dual number matrix may have no eigenvalue at all. An algorithm based upon the Collatz minimax theorem is constructed. The convergence of the algorithm is studied. We give an upper bound on the distance of stationary states between the dual Markov chain and the perturbed Markov chain. Numerical results on both synthetic examples and dual Markov chain including some real world examples are reported.

歡迎廣大師生參加！