數(shù)據(jù)擬合方法研究氣溫變化規(guī)律

數(shù)值計(jì)算》實(shí)驗(yàn)報(bào)告實(shí)驗(yàn)名稱(chēng)數(shù)據(jù)擬合方法研究氣溫變化規(guī)律姓名羅光光學(xué)號(hào)1402120418成績(jī)學(xué)院：軟件學(xué)院專(zhuān)業(yè)：軟件工程班級(jí)：12級(jí)4班實(shí)驗(yàn)報(bào)告內(nèi)容要求:實(shí)驗(yàn)三：編寫(xiě)多項(xiàng)式擬合程序。并用該程序解決下列問(wèn)題：假定某天的氣溫變化記錄如下表，試用最小二乘方法找出這一天的氣溫變化規(guī)律。t/h12345678910111213T/°C14141414151618202223252831t/h1415161718192021222324T/°C3231292725242220181716考慮下列類(lèi)型函數(shù)，計(jì)算誤差平方和，并作圖比較效果。1?二次函數(shù)2?三次函數(shù)3?四次函數(shù)4?函數(shù)C=ae(-b(t-c)2)(提高：非線性擬合問(wèn)題)實(shí)驗(yàn)?zāi)康模??理解數(shù)據(jù)擬合的基本概念，基本方法；2?掌握最小二乘法的基本原理,并學(xué)會(huì)通過(guò)計(jì)算機(jī)解決實(shí)際問(wèn)題.實(shí)驗(yàn)原理：利用最小二乘法來(lái)解決實(shí)際遇到的問(wèn)題，并解決問(wèn)題實(shí)驗(yàn)環(huán)境：PC機(jī),MATLAB程序?qū)嶒?yàn)過(guò)程(編寫(xiě)的程序)(1)二次函數(shù)?fun2=inline('c(l)*x.A2+c(2)*x+c(3)','c','x')fun2=Inlinefunction:fun2(c,x)=c(1)*x.A2+c(2)*x+c(3)>>x=0:24;>>y=[15141414141516182022232528313231292725242220181716];

>>c=lsqcurvefit(fun2,[00O],x,y)Optimizationterminated:relativefunctionvaluechangingbylessthanOPTIONS.TolFun.c=-0.09362.59438.4157>>poly2str(c,'x')ans=-0.093609xA2+2.5943x+8.4157(2)三次函數(shù)>>fun2=inline('c(1)*x.A3+c(2)*x.A2+c(3)*x+c(4)','c','x')fun2=Inlinefunction:fun2(c,x)=c(1)*x.A3+c(2)*x.A2+c(3)*x+c(4)>>x=0:24;y=[15141414141516182022232528313231292725242220181716];>>c=lsqcurvefit(fun2,[0000],x,y)Maximumnumberoffunctionevaluationsexceeded;increaseoptions.MaxFunEvalsc=-0.00710.15970.248712.4001>>poly2str(c,'x')ans=-0.0070916xA3+0.15971x2+0.24868x+12.4001(3)鐘形函數(shù)f(t)=aeb(t-⑷2>>fun2=inline('c(1)*exp(c(2)*(t-14).A2)','c','t')fun2=Inlinefunction:fun2(c,t)=c(1)*exp(c(2)*(t-14).A2)>>t=0:24;y=[15141414141516182022232528313231292725242220181716];>>c=lsqcurvefit(fun2,[0,0],t,y)Optimizationterminated:relativefunctionvaluechangingbylessthanOPTIONS.TolFun.27.9628-0.0058%a=27.962827.9628-0.0058%a=27.9628b=-0.00584fl0Iff30in3344卜先::3D20lfr4fl0Iff30in3344卜先::3D20lfr<01010五、實(shí)驗(yàn)結(jié)果及分析此地的氣溫隨著時(shí)間的推遲