實(shí)驗(yàn)誤差計(jì)算與什么是數(shù)值計(jì)算方法及應(yīng)用doc

1、《數(shù)值計(jì)算方法》實(shí)驗(yàn)報(bào)告1什么是數(shù)值計(jì)算方法及應(yīng)用與誤差計(jì)算什么是數(shù)值計(jì)算方法及應(yīng)用與誤差計(jì)算1什么是數(shù)值計(jì)算方法及應(yīng)用什么是數(shù)值計(jì)算方法及應(yīng)用計(jì)算數(shù)學(xué)也叫做數(shù)值計(jì)算方法或數(shù)值分析。主要內(nèi)容包括代數(shù)方程、線性代數(shù)方程組、微分方程的數(shù)值解法，函數(shù)的數(shù)值逼近問題，矩陣特征值的求法，最優(yōu)化計(jì)算問題，概率統(tǒng)計(jì)計(jì)算問題等等，還包括解的存在性、唯一性、收斂性和誤差分析等理論問題。數(shù)值計(jì)算方法是一種研究并解決數(shù)學(xué)問題的數(shù)值近似解方法是在計(jì)算機(jī)上使用的

2、解數(shù)學(xué)問題的方法，簡稱計(jì)算方法。在科學(xué)研究和工程技術(shù)中都要用到各種計(jì)算方法。例如，在航天航空、地質(zhì)勘探、汽車制造、橋梁設(shè)計(jì)、天氣預(yù)報(bào)和漢字字樣設(shè)計(jì)中都有計(jì)算方法的蹤影.Numericalanalysisinvolvesthestudyofmethodsofcomputingnumericaldata.Inmanyproblemsthisimpliesproducingasequenceofapproximationsbyrepeatin

3、gtheprocedureagainagain.Peoplewhoemploynumericalmethodsfsolvingproblemshavetowryaboutthefollowingissues:therateofconvergence(howlongdoesittakefthemethodtofindtheanswer)theaccuracy(evenvalidity)oftheanswerthecompletenesso

4、ftheresponse(doothersolutionsinadditiontotheonefoundexist).Numericalmethodsprovideapproximationstotheproblemsinquestion.Nomatterhowaccuratetheyare，theydonotinmostcasesprovidetheexactanswer.Insomeinstanceswkingouttheexact

5、answerbyadifferentapproachmaynotbepossiblemaybetootimeconsumingitisinthesecaseswherenumericalmethodsaremostoftenused.Theeverincreasingadvancesincomputertechnologyhasenabledmanyinscienceengineeringtoapplynumericalmethodst

6、osimulatephysicalphenomena.Numericalmethodsareoftendividedintoelementaryonessuchasfindingtherootofanequationintegratingafunctionsolvingalinearsystemofequationstointensiveoneslikethefiniteelementmethod.Intensivemethodsare

7、oftenneededfthesolutionofpracticalproblemstheyoftenrequirethesystematicapplicationofarangeofelementarymethodsoftenthoussmillionsoftimesover.Inthedevelopmentofnumericalmethodssimplificationsneedtobemadetoprogresstowardsas

8、olution:fexamplegeneralfunctionsmayneedtobeapproximatedbypolynomialscomputerscannotgenerallyrepresentnumbersexactlyanyway.Asaresultnumericalmethodsdonotusuallygivetheexactanswertoagivenproblemtheycanonlytendtowardsasolut

9、iongettingclosercloserwitheachiteration.Numericalmethodsaregenerallyonlyusefulwhentheyareimplementedoncomputerusingacomputerprogramminglanguage.Inthestudyofnumericalmethodswecanmakeageneraldistinctionbetweenasetofmethods

10、suchassolvinglinearsystemsofequationssolvingmatrixeigenvalueproblemsinterpolationnumericalintegrationfindingtherootszerosofequationswhichcanbesomewhat《數(shù)值計(jì)算方法》實(shí)驗(yàn)報(bào)告31.實(shí)驗(yàn)描述實(shí)驗(yàn)描述1根據(jù)習(xí)題12和習(xí)題13構(gòu)造算法和MATLAB程序，以便精確計(jì)算所有情況下的二次方程的根，包括

11、的情況。24bbac??2參照1.25對3個(gè)差分方程計(jì)算出前十個(gè)數(shù)值的近似值，構(gòu)造列表和圖形。誤差算法分別為.nnxr?nnxp?nnxq?2.2.實(shí)驗(yàn)內(nèi)容實(shí)驗(yàn)內(nèi)容1設(shè)，，且有方程。通過如下二次根公式可解出方程的根：0a?24ac0b2=0axbxc（1）2244x1=2=22bbacbbacxaa????這些根還可通過下列等價(jià)公式解出：（2）22221=2=44ccxxbbacbbac??2對下列三個(gè)差分方程計(jì)算出前10個(gè)數(shù)值近似值。

12、在每種情況下引入一個(gè)小的初始誤差。如果沒有初始誤差，則每個(gè)差分方程將生成序列。用MATLAB構(gòu)造生成圖表。=112nn???????(a)其中n=12…011=0.994=2nnrrr(b)，其中n=23…011231=1=0.497=22nnnppppp(c)其中n=23…01125=1=0.497=2nnnqqqqq3.3.實(shí)驗(yàn)結(jié)果及分析實(shí)驗(yàn)結(jié)果及分析1.二次方程的的求根根據(jù)習(xí)題12所述，若b0兩個(gè)根為==若b0兩個(gè)根為1x224c