用mathematics实现拉格朗日插值及其图形化.docx

两点的线性插值直接运用公式给出1x0=0.5;y0=-0.693147;x1=0.6;y1=-0.510826;fx_:=(x-x1)/(x0-x1)*y0+(x-x0)/(x1-x0)*y1;f0.54-0.620219p1=Plotfx,x,-1,1;p2=ListPlot0.54,-0.620219,PlotStyleRGBColor1,0,1,PointSize0.02;Showp1,p211111111111111111111111111111111Clearx0,y0;运用for循环进行两点几多点的拉格朗日插值并将其图形化m=0.5,-0.693147,0.6,-0.510826;y0=0;Fori=1,iLengthm,i+,y=1;Forj=1,jLengthm,j+, Ifij,y=y*(x0-mj,1)/(mi,1-mj,1);y0=y0+mi,2*y;Printy0;y0/.x00.546.93147 (-0.6+x0)-5.10826 (-0.5+x0)-0.620219p1=ListPlotm,PlotStyleRGBColor1,0,0,PointSize0.02;p2=Ploty0,x0,-1,1,PlotStyleRGBColor1,1,0,Thickness0.01;Showp1,p222222222222222222222222222222222222222222222m=1,3,2,6,3,9;x0=1.5;y0=0;Fori=1,iLengthm,i+,y=1;Forj=1,jLengthm,j+, Ifji,y=y*(x0-mj,1)/(mi,1-mj,1);y0=y0+mi,2*y;y04.5 222222222222222222222222m=1,1.2,3,2.6,5,3.8,6,5.5,7,6.7,8,9.8,10,12;x0=9;y0=0;Fori=1,iLengthm,i+,y=1;Forj=1,jLengthm,j+, Ifji,y=y*(x0-mj,1)/(mi,1-mj,1);y0=y0+mi,2*y;y015.2343222222222222222222222222222222222222222222222222223333333333333333Clearx0,y0m=1,3,2,6,3,9;y0=0;Fori=1,iLengthm,i+,y=1;Forj=1,jLengthm,j+, Ifji,y=y*(x0-mj,1)/(mi,1-mj,1);y0=y0+mi,2*y;Printy0;y0/.x01.53/2 (2-x0) (3-x0)+6 (3-x0) (-1+x0)+9/2 (-2+x0) (-1+x0)4.5p3=ListPlotm,PlotStyleRGBColor1,0,0,PointSize0.02;p4=Ploty0,x0,-10,10,PlotStyleRGBColor1,1,0,Thickness0.01;Showp3,p433333333333333333333333333333333Clearx0,y0m=1,4,3,10,5,116,7,150,9,201;y0=0;Fori=1,iLengthm,i+,y=1;Forj=1,jLengthm,j+, Ifji,y=y*(x0-mj,1)/(mi,1-mj,1);y0=y0+mi,2*y;Printy0;y0/.x0101/96 (3-x0) (5-x0) (7-x0) (9-x0)+5/48 (5-x0) (7-x0) (9-x0) (-1+x0)+29/16 (7-x0) (9-x0) (-3+x0) (-1+x0)+25/16 (9-x0) (-5+x0) (-3+x0) (-1+x0)+67/128 (-7+x0) (-5+x0) (-3+x0) (-1+x0)42503/128p5=ListPlotm,PlotStyleRGBColor1,0,0,PointSize0.02;p6=Ploty0,x0,-10,10,PlotStyleRGBColor1,1,0,Thickness0.01;p9=ListPlotx0,y0,PlotStyleRGBColor1,0,0,PointSize0.02;Showp5,p644444444444444444444444444444444444444444444444444444444444444444444444这是分段线性插值4444444444444444444444444444444Clearx0,y0m=1,4,3,10,5,116,7,150,9,201;y0=0;x0=3.5;Forr=2,rLengthm,r+,Ifmr-1,1=x0mr,1,n=mr-1,r;Fori=1,iLengthn,i+,y=1;Forj=1,jLengthn,j+, Ifji,y=y*(x0-nj,1)/(ni,1-nj,1);y0=y0+ni,2*y;nPrinty03,10,5,11636.5p7=ListPlotm,PlotJoinedTrue,PlotStyleRGBColor1,0,0,Thickness0.01;p8=ListPlotx0,