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報(bào)告題目：應(yīng)用統(tǒng)計(jì)國(guó)家一流專業(yè)建設(shè)系列講座——The upper-crossing/solution (US) algorithm for root-finding with strongly stable convergence(具有強(qiáng)穩(wěn)定收斂性的求一元非線性方程之根的上穿求解算法)

主講人：田國(guó)梁（南方科技大學(xué)）

時(shí)間：2022年11月22日（周二）10:00 a.m.

形式：線上講座（騰訊會(huì)議）      

會(huì)議ID：888-695-182

主辦單位：統(tǒng)計(jì)與數(shù)學(xué)學(xué)院

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. Especially, because of the property of strongly stable convergence, the US algorithm could be one of the powerful tools for solving an equation with multiple roots.

主講人簡(jiǎn)介：

田國(guó)梁博士曾在美國(guó)馬里蘭大學(xué)從事醫(yī)學(xué)統(tǒng)計(jì)研究六年, 在香港大學(xué)統(tǒng)計(jì)與精算學(xué)系任副教授八年, 從2016年6月至今在南方科技大學(xué)統(tǒng)計(jì)與數(shù)據(jù)科學(xué)系任教授,、博士生導(dǎo)師,、副系主任。他目前的研究方向?yàn)镋M/MM/US算法在統(tǒng)計(jì)中的應(yīng)用,、(0, 1) 區(qū)間上連續(xù)比例數(shù)據(jù)以及多元連續(xù)比例數(shù)據(jù)的統(tǒng)計(jì)分析,、多元零膨脹計(jì)次數(shù)據(jù)分析, 在國(guó)外發(fā)表140篇SCI論文、出版3本英文專著,、在科學(xué)出版社出版英文教材2本,。他是四個(gè)國(guó)際統(tǒng)計(jì)期刊的副主編。主持國(guó)家自然科學(xué)基金面上項(xiàng)目二項(xiàng),、主持深圳市穩(wěn)定支持面上項(xiàng)目一項(xiàng),、參加國(guó)家自然科學(xué)基金重點(diǎn)項(xiàng)目一項(xiàng)。