應學院邀請，南方科技大學田國梁教授将在線作學術報告。
報告題目：The upper-crossing/solution (US) algorithm for root-finding with strongly stable convergence
報告摘要：In this paper, we propose a new and broadly applicable root-finding method, called as the upper-crossing/solution (US) algorithm, which belongs to the category of non-bracketing (or open domain) methods. The US algorithm is a general principle for iteratively seeking the unique root of a non-linear equation g(θ) = 0 and its each iteration consists of two steps: an upper-crossing step (U-step) and a solution step (S-step), where the U-step finds an upper-crossing function or a -function [whose form depends on being the -th iteration of ] based on a new notion of so-called changing direction inequality, and the S-step solves the simple -equation to obtain its explicit solution . The US algorithm holds two major advantages: (i) It strongly stably converges to the root ; and (ii) it does not depend on any initial values, in contrast to Newton's method. The key step for applying the US algorithm is to construct one simple -function such that an explicit solution to the -equation is available. Based on the first-, second- and third-derivative of , three methods are given for constructing such -functions. We show various applications of the US algorithm in calculating quantile in continuous distributions, calculating exact -values for skew null distributions, and finding maximum likelihood estimates of parameters in a class of continuous/discrete distributions. The analysis of the convergence rate of the US algorithm and some numerical experiments are also provided.
報告時間：2022年11月13日09:00
報告地點：騰訊會議号(252958927)
邀 請 人：田玉柱副教授 肖鴻民教授
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報告人簡介
田國梁博士曾在美國馬裡蘭大學從事醫學統計研究六年, 在香港大學統計與精算學系任副教授八年, 從2016年6月至今在南方科技大學統計與數據科學系任教授、博士生導師、副系主任。他目前的研究方向為EM/MM/US算法在統計中的應用、(0,1)區間上連續比例數據以及多元連續比例數據的統計分析、多元零膨脹計次數據分析, 在國外發表140篇SCI論文、出版3本英文專著、在科學出版社出版英文教材2本。他是四個國際統計期刊的副主編。主持國家自然科學基金面上項目二項、主持深圳市穩定支持面上項目一項、參加國家自然科學基金重點項目一項。
