应学院邀请，南方科技大学田国梁教授将在线作学术报告。
报告题目：The upper-crossing/solution (US) algorithm for root-finding with strongly stable convergence
报告摘要：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.
报告时间：2022年11月13日09:00
报告地点：腾讯会议号(252958927)
邀 请 人：田玉柱副教授 肖鸿民教授
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报告人简介
田国梁博士曾在美国马里兰大学从事医学统计研究六年, 在香港大学统计与精算学系任副教授八年, 从2016年6月至今在南方科技大学统计与数据科学系任教授、博士生导师、副系主任。他目前的研究方向为EM/MM/US算法在统计中的应用、(0,1)区间上连续比例数据以及多元连续比例数据的统计分析、多元零膨胀计次数据分析, 在国外发表140篇SCI论文、出版3本英文专著、在科学出版社出版英文教材2本。他是四个国际统计期刊的副主编。主持国家自然科学基金面上项目二项、主持深圳市稳定支持面上项目一项、参加国家自然科学基金重点项目一项。
