SHANGHAIUNIVERSITY畢業(yè)設(shè)計(jì)（論文）UNDERGRADUATEPROJECT(THESIS)題目:從Chebyshev到Bernstein:多項(xiàng)式初探學(xué)院理學(xué)院專業(yè)信息與計(jì)算數(shù)學(xué)指導(dǎo)教師張建軍起訖日期7月8日起12月15日止上海大學(xué)畢業(yè)設(shè)計(jì)(論文)1目錄摘要:-2ABSTRACT-31.緒論-42.第一章-63.第二章-134.結(jié)論-24上海大學(xué)畢業(yè)設(shè)計(jì)(論文)2Chebyshev到Bernstein:多項(xiàng)式初探摘要多項(xiàng)式問(wèn)題的研究是一個(gè)古老但非常有意義的問(wèn)題，它在現(xiàn)代數(shù)學(xué)中占有重要地位。多項(xiàng)式方程的求根，函數(shù)的多項(xiàng)式逼近等等問(wèn)題是應(yīng)用數(shù)學(xué)，計(jì)算數(shù)學(xué)中的一個(gè)重要研究問(wèn)題，它不僅在理論上，而且在實(shí)際問(wèn)題中都有重要應(yīng)用。本課題研究多項(xiàng)式的大小對(duì)多項(xiàng)式根的位置的影響，考察多項(xiàng)式對(duì)于解的位置變動(dòng)的敏感性。我們從Chebyshev多項(xiàng)式入手，研究多項(xiàng)式的大小對(duì)多項(xiàng)式根的位置的影響。本課題的主要內(nèi)容是對(duì)Chebyshev多項(xiàng)式和Bernstein多項(xiàng)式做進(jìn)一步深入分析，了解他們的有用的重要性質(zhì)。給出一些有意義新的問(wèn)題的結(jié)論。本論文的創(chuàng)新點(diǎn)之一就是對(duì)多項(xiàng)式的數(shù)域的擴(kuò)充到復(fù)數(shù)的情況。巧妙地從兩個(gè)典型的多項(xiàng)式，車比雪夫多項(xiàng)式和伯恩斯坦多項(xiàng)式出發(fā)，拋磚引玉地深入問(wèn)題。尤其在借鑒數(shù)值逼近中最小多項(xiàng)式的概念引出最大多項(xiàng)式的概念后對(duì)多項(xiàng)式限制一定條件后逐步深入問(wèn)題。關(guān)鍵詞：最大（最小）無(wú)窮范數(shù)、（最大）最小多項(xiàng)式、根的擾動(dòng)、根的位置關(guān)系、Chebyshev、Bernstein上海大學(xué)畢業(yè)設(shè)計(jì)(論文)3ABSTRACTPolynomialproblemofresearchisanancientbutverymeaningfulquestions,itisinthemodernmathematicsplaysanimportantrole.Polynomialequationextractroots,functionofpolynomialapproximationetcproblemisappliedmathematics,computationalmathematicsoneoftheimportantresearchproblems,itnotonlytheoretically,butinactualprobleminallhaveimportantapplications.Thistopicresearchpolynomialsizeonthepositionoftheinfluenceofpolynomialroot,investigatesthepositionvariationofpolynomialforsolutionofsensitivity.WeChebyshevpolynomial,startingfromresearchpolynomialsizeonthepositionoftheinfluenceofpolynomialroot.ThistopicismaincontentonChebyshevpolynomialsandBernsteinpolynomialdofurtheranalysis,understandtheirusefulimportantproperties.Givesomemeaningfulnewproblemconclusion.Thisthesisisoneoftheinnovationpointsofpolynomialnumberdomainexpansiontopluralssituation.Ablyfromtwotypicalpolynomials,carthansnowCardiffpolynomialsandBernsteinpolynomialembarks,derivedeeperintoquestion.Especiallyindrawinganumericalapproachintheconceptofminimumpolynomialsdrawntotheconceptofmaximumpolynomialafterpolynomiallimitaftercertainconditiondeepensproblem.Keywords:Thebiggest(mi