数值计算编程20个

1、P11，第一题PrivateSubForm_Click()Dima,b,x,sAsDoublea=1b=2s=0.001Dox=(a+b)/2If(x人3-x-1)*(a人3-a-1)<0Thenb=xElsea=xEndIfLoopUntilAbs(x人3-x-1)<sPrintxPrintx人3-x-1EndSub结果：1.2、P12，第五题PrivateSubForm_Click()Dima,x,sAsDoublea=8s=0.001x=aDop=xx=(p+a/p)/2LoopUntilAbs(x-p)<sPrintxEndSub结果：2.9863、程序：PrivateSubForm_Click()DimiAsIntegerDimt,a(0To3),pAsDoublet=2Fori=0To3a(i)=InputBox("x("&i&")=")Nextip=a(3)Fori=2To0Step-1p=p*t+a(i)NextiPrintpEndSub结果：494、程序：PrivateSubForm_Click()Dima,b,sAsDoublea=0.2b=1.34s=(a+b)/2DoIfa*(1-a)*s*(1-s)<0Thenb=sElsea=sEndIfs=(a+b)/2LoopUntilb-a<0.01PrintsEndSub结果：0.9971093755、程序：PrivateSubForm_click()Dimx,s,pAsDoubleDimiAsIntegerx=101s=10p=1/2/10i=1Dos=s+pp=p/2*(-1)/100*(2*i-1)i=i+1LoopUntilp<0.01PrintsEndSub结果：10.056、拉格朗日：PrivateSubForm_Click()Dimi,j,nAsIntegerDimx(1To100),y(1To100),p,s,tAsDoublet=2.5n=3Fori=1Tonx(i)=InputBox("x("&i&")=")y(i)=InputBox("y("&i&")=")Nextis=0Fori=1Tonp=1Forj=1TonIfi<>jThenp=p*(t-x(j))/(x(i)-x(j))EndIfNextjs=s+p*y(i)NextiPrintsEndSub结果：67、课堂埃尔米特插值程序：PrivateSubForm_Activate()Dimx0,y0,x1,y1,g0,g1AsDoublex0=0y0=0x1=1y1=1g0=0g1=2x=0.5a0=-2/(xO-xl)人3bO=1/(xO-xl)人2+2*xO/(xO-xl)人3al=-2/(xl-xO)人3bl=2*xl/(xl-xO)人3+l/(xl-xO)人2kO=l/(xO-xl)人2k1=1/(xl-xO)人2=(x-xl)人2*(aO*x+bO)=(x-xO)人2*(al*x+bl)ggO=kO*(x-xO)*(x-xl)人2ggl=kl*(x-xO)人2*(x-xl)y=1O*yO+1l*yl+ggO*gO+ggl*glPrintyEndSub结果：O.258、第一个：样条函数：PrivateSubForm_Activate()Dimx(3),y(3),mO,ml,m2AsDoub1eDimiAsIntegerFori=OTo2x(i)=iy(i)=i*iNextimO=Om2=4hO=x(l)-x(O)hl=x(2)-x(l)a=2/hOb=4/hO+4/hlc=2/hld=(-6*y(l)+6*y(2))/hl人2-(6*y(O)-6*y(l))/hO人2ml=(d-a*mO-c*m2)/bPrintmlEndSub结果：29、牛顿插值：DimkAsIntegerPrivateSubCombol_C1ick()DimiAsIntegerk=CInt(Combol.Text)Fori=OTo9Textl(2*i).Visib1e=Fa1seTextl(2*i+l).Visib1e=Fa1seLabe1(i).Visib1e=Fa1seNextiFori=0Tok-1WithLabel(i).Visible=True.Top=1560+400*i.Caption="第"&i+1&"点：".Left=120EndWithWithText1(2*i).Visible=True.Left=800.Top=1500+400*iEndWithWithText1(2*i+1).Visible=True.Left=1500.Top=1500+400*iEndWithNextiEndSubPrivateSubCommand1_Click()DimiAsIntegerDimsAsDoubles=0Fori=0Tok-1s=s+ff(i)*f1(Text3.Text,i)NextiText2.Text=sEndSubPrivateSubCommand2_Click()EndEndSubPrivateSubForm_Load()DimiAsIntegerFori=2To10Combo1.AddItemiNextiEndSubFunctionff(ByValnAsInteger)DimiAsIntegerDimsAsDoubles=0Ifn=0Thenff=Text1(1).TextExitFunctionEndIfFori=0Tons=s+Text1(2*i+1).Text/f(i,n)Nextiff=sEndFunctionFunctionf(ByValpAsInteger,ByValnAsInteger)DimiAsIntegerDimsAsDoubles=1Fori=0TonIfi<>pThens=s*(Text1(2*p).Text-Text1(2*i).Text)EndIfNextif=sEndFunctionFunctionf1(ByValxAsDouble,ByValnAsInteger)DimiAsIntegerDimsAsDoubleIfn=0Thenf1=1ExitFunctionEndIfs=1Fori=0Ton-1s=s*(x-Text1(2*i).Text)Nextif1=sEndFunction结果：带入(1,1)，(2,4)，(3,7)，(4,8)，(5,6)得到变量为3.5时，插值结果为7.835937510、复化辛普生算法：PrivateSubCommand1_Click()Dimi,nAsIntegerDims,h,xAsDoublea=InputBox("请输入左端点a：")b=InputBox("请输入右端点b：")n=InputBox("请输入分段数n：")h=(b-a)/ns=f(b)-f(a)x=aFori=1Tonx=x+h/2s=s+4*f(x)x=x+h/2s=s+2*f(x)Nextis=h/6*sText1.Text=sEndSubFunctionf(ByValxAsDouble)Ifx=0Thenf=1ExitFunctionEndIff=Sin(x)/xEndFunction结果：当输入区间为(0,1)，分8段，运行结果是0.194311、p153第6题PrivateSubForm_Load()Dims,t,eAsDoubleDimi,kAsIntegert=0k=0s=(t+2)人0.5e=0.001Fori=0To20IfAbs(s-t)<eThenk=1ExitForEndIft=ss=(t+2)人0.5NextiText1.Text=sEndSub结果：1.82912、p154第18题DimaAsDoublePrivateSubForm_Load()Dimx0,x,eAsDoubleDimiAsIntegerx=5e=0.000001a=InputBox("a=")Fori=0To20x0=xText1.Text=Text1.Text&vbCrLf&f1(x0)Iff1(x0)=0ThenExitForEndIfx=x0-f(x0)/f1(x0)IfAbs(x-x0)<eThenExitForEndIfNextiIfi=20ThenMsgBox"迭代失败！"EndEndIfText1.Text=xEndSubFunctionf(ByValxAsDouble)f=x人3-aEndFunctionFunctionf1(ByValxAsDouble)fl=3*x人2EndFunction结果：2.188l3、pl55第24题牛顿法PrivateSubForm_Load()Dimx0,eAsDoubleDimiAsIntegerx0=0e=0.000001n=20Iff1(x0)=0ThenMsgBox"奇异"EndEndIfFori=oTo20x0=xIff1(x)=0ThenMsgBox"奇异"EndEndIfx=x0-f(x0)/f1(x0)IfAbs(x-x0)<eThenExitForEndIfNextiIfi=20ThenMsgBox"迭代失败！"EndEndIfText1.Text=xEndSubFunctionf(ByValxAsDouble)f=x人3+2*x人2+10*x-20EndFunctionFunctionf1(ByValxAsDouble)fl=3*x人2+4*x+10EndFunction结果：1.13714、p155第24题弦截法PrivateSubForm_Load()Dimx0,x1,eAsDoubleDimiAsIntegerx0=0e=0.000001n=20Iff1(x0)=0ThenMsgBox"奇异"EndEndIfx1=x0-f(x0)/f1(x0)Fori=oTo20x=x1-f(x1)/(f(x1)-f(x0))*(x1-x0)IfAbs(x-x1)<eThenExitForEndIfx1=xNextiIfi=20ThenMsgBox"迭代失败！"EndEndIfText1.Text=xEndSubFunctionf(ByValxAsDouble)f=x人3+2*x人2+10*x-20EndFunctionFunctionf1(ByValxAsDouble)fl=3*x人2+4*x+10EndFunction结果：1.56215、p155第24题快速弦截法PrivateSubForm_Load()Dimx0,x1,eAsDoubleDimiAsIntegerx0=0e=0.000001n=20Iff1(x0)=0ThenMsgBox"奇异"EndEndIfx1=x0-f(x0)/f1(x0)Fori=oTo20x0=x1x1=xx=x1-f(x1)/(f(x1)-f(x0))*(x1-x0)IfAbs(x-x1)<eThenExitForEndIfNextiIfi=20ThenMsgBox"迭代失败！"EndEndIfText1.Text=xEndSubFunctionf(ByValxAsDouble)f=x人3+2*x人2+10*x-20EndFunctionFunctionf1(ByValxAsDouble)fl=3*x人2+4*x+10EndFunction结果：1.49616、消去法DimnAsIntegerDima(1To10,1To10),b(1To10),x(1To10)AsDoublePrivateSubCombo1_Click()Dimi,jAsIntegerFori=1To100Text1(i).Visible=FalseNextiFori=1To10Text2(i).Visible=FalseText3(i).Visible=FalseNextin=Combo1.TextFori=1TonForj=1TonWithText1((i-1)*n+j).Visible=True.Top=500*i+200.Left=500*j.Height=300EndWithNextjWithText2(i).Visible=True.Top=500*i+200.Left=500*n+800.Height=300EndWithWithText3(i).Visible=True.Top=500*i+200.Left=500*n+1800.Width=700.Height=300EndWithNextiEndSubPrivateSubCommand1_Click()Dimi,j,kAsIntegerDims,rAsDoubleFori=1TonForj=1Tona(i,j)=Text1((i-1)*n+j).TextNextjb(i)=Text2(i).TextNextiFori=1Ton-1Forj=i+1Tonr=a(j,i)/a(i,i)Fork=iTona(j,k)=a(j,k)-r*a(i,k)Nextkb(j)=b(j)-r*b(i)NextjNextiFori=nTo1Step-1s=b(i)Ifi<>nThenForj=iTons=s-a(i,j)*x(j)NextjEndIfx(i)=s/a(i,i)Text3(i).Text=x(i)NextiEndSubPrivateSubCommand2_Click()EndEndSubPrivateSubForm_Load()DimiAsIntegerFori=2To10Combo1.AddItemiNextiEndSub结果：选择求解未知数个数为3,再依次输入A={2,-1,3；4,2,5；1,2,0；}B={1,4,7；}得到x={9，-1，-6}17、追赶法PrivateSubCommand1_Click()Dimi,j,kAsIntegerDimaa(1To4),bb(1To4),cc(1To4),dd(1To4),xx(1To4),g(1To4),f(1To4)AsDoubleDims,rAsDoubleFori=1To4Ifi=1Thenaa(i)=0Elseaa(i)=a(i).TextEndIfbb(i)=b(i).TextIfi=4Thencc(i)=0Elsecc(i)=c(i).TextEndIfdd(i)=d(i).TextNextig(1)=dd(1)/bb(1)f(1)=-cc(1)/bb(1)Fori=2To4g(i)=(dd(i)-aa(i)*g(i-1))/(aa(i)*f(i-1)+bb(i))f(i)=-cc(i)/(aa(i)*f(i-1)+bb(i))Nextixx(4)=g(4)x(4).Text=xx(4)Fori=3To1Step-1xx(i)=g(i)+f(i)*xx(i+1)x(i).Text=xx(i)NextiEndSubPrivateSubCommand2_Click()EndEndSub结果:依次输入方程组系数A={1,1；1,2,1；1,2,3；1,2；},B={3,8,20,ll}得到结果为X={1,2,3,4；}18、高斯-赛德尔程序如下：PrivateSubCommand1_Click()Dimi,jAsIntegerDimk,t(1To3),s,a(1To3,1To3),b(1To3),x(1To3)AsDoubleFori=1To3Forj=1To3a(i,j)=Text1(i*3+j-3).TextNextjb(i)=Text2(i).Textx(i)=0Nextik=1DoUntilk<0.0001Fori=1To3s=b(i)Forj=1To3Ifj<>iThenText4.Text=ss=s-a(i,j)*x(j)Text5.Text=sEndIfNextjt(i)=s/a(i,i)Ifi=1Thenk=Abs(t(i)-x(i))ElseIfAbs(t(i)-x(i))>kThenk=Abs(t(i)-x(i))EndIfx(i)=t(i)NextiLoopFori=1To3Text3(i).Text=x(i)NextiEndSub运行结果:输入系数A={7,5,-3;5,7,1;2,1,7;}B={2,4,-11}得到X={-1.727,2.000,-1.363}19、迭代法程序如下：PrivateSubCommand1_Click()Dimi,jAsIntegerDimk,t(1To3),s,a(1To3,1To3),b(1To3),x(1To3)AsDoubleFori=1To3Forj=1To3a(i,j)=Text1(i*3+j-3).TextNextjb(i)=Text2(i).Textx(i)=0Nextik=1DoUntilk<0.0001Fori=1To3s=b(i)Forj=1To3Ifj<>iThenText4.Text=ss