实验1_误差计算与什么是数值计算方法及应用.doc

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1、《数值计算方法》实验报告11什么是数值计算方法及应用与误差计算1．什么是数值计算方法及应用计算数学也叫做数值计算方法或数值分析。主要内容包括代数方程、线性代数方程组、微分方程的数值解法，函数的数值逼近问题，矩阵特征值的求法，最优化计算问题，概率统计计算问题等等，还包括解的存在性、唯一性、收敛性和误差分析等理论问题。数值计算方法,是一种研究并解决数学问题的数值近似解方法,是在计算机上使用的解数学问题的方法，简称计算方法。在科学研究和工程技术中都要用到各种计算方法。例如，在航天航空、地质勘探、汽车制造、桥梁设计、天气预报和汉字

2、字样设计中都有计算方法的踪影.《数值计算方法》实验报告11《数值计算方法》实验报告11Numericalanalysisinvolvesthestudyofmethodsofcomputingnumericaldata.Inmanyproblemsthisimpliesproducingasequenceofapproximationsbyrepeatingtheprocedureagainandagain.Peoplewhoemploynumericalmethodsforsolvingproblemshavetowor

3、ryaboutthefollowingissues:therateofconvergence(howlongdoesittakeforthemethodtofindtheanswer),theaccuracy(orevenvalidity)oftheanswer,andthecompletenessoftheresponse(doothersolutions,inadditiontotheonefound,exist).Numericalmethodsprovideapproximationstotheproblemsin

4、question.Nomatterhowaccuratetheyare，theydonot,inmostcases,providetheexactanswer.Insomeinstancesworkingouttheexactanswerbyadifferentapproachmaynotbepossibleormaybetootimeconsuminganditisinthesecaseswherenumericalmethodsaremostoftenused.Theever-increasingadvancesinc

5、omputertechnologyhasenabledmanyinscienceandengineeringtoapplynumericalmethodstosimulatephysicalphenomena.Numericalmethodsareoftendividedintoelementaryonessuchasfindingtherootofanequation,integratingafunctionorsolvingalinearsystemofequationstointensiveoneslikethefi

6、niteelementmethod.Intensivemethodsareoftenneededforthesolutionofpracticalproblemsandtheyoftenrequirethesystematicapplicationofarangeofelementarymethods,oftenthousandsormillionsoftimesover.Inthedevelopmentofnumericalmethods,simplificationsneedtobemadetoprogresstowa

7、rdsasolution:forexamplegeneralfunctionsmayneedtobeapproximatedbypolynomialsandcomputerscannotgenerallyrepresentnumbersexactlyanyway.Asaresult,numericalmethodsdonotusuallygivetheexactanswertoagivenproblem,ortheycanonlytendtowardsasolutiongettingcloserandcloserwithe

8、achiteration.Numericalmethodsaregenerallyonlyusefulwhentheyareimplementedoncomputerusingacomputerprogramminglanguage.Inthestudyofnumericalmethods,wecanm