計算方法實驗報告-3

曲線擬合問題實驗報告

一、實驗要求1、已知實驗數(shù)據(jù)如下表2、求擬合多項式：=分別對n=2,3,4,5,6進行數(shù)值計算3、且根據(jù)各自的偏差平方和分析擬合效果原始數(shù)據(jù)xyxy51.0029300.9979101.0023350.9978151.0000400.9981200.99450.9987250.9983500.9996

二、實驗內(nèi)容1.源代碼及具體實現(xiàn)>>x=5:5:50;y=[1.0029,1.0023,1.000,0.9990,0.9983,0.9979,0.9978,0.9981,0.9987,0.9996];plot(x,y,'*'),pause2階擬合在MATLAB運行窗口輸入p2=polyfit(x,y,2);y2=polyval(p2,x);holdon,plot(x,y2,'-.'),gtext('y2'),pause3階擬合在MATLAB運行窗口輸入p3=polyfit(x,y,3);y3=polyval(p3,x);holdon,plot(x,y3,'m'),holdon,gtext('y3'),pause4階擬合在MATLAB運行窗口輸入p4=polyfit(x,y,4);y4=polyval(p4,x);holdon,plot(x,y4,'g'),gtext('y4'),pause5階擬合在MATLAB運行窗口輸入p5=polyfit(x,y,5);y5=polyval(p5,x);holdon,plot(x,y5,'r'),gtext('y5'),pause6階擬合在MATLAB運行窗口輸入p6=polyfit(x,y,6);y6=polyval(p6,x);holdon,plot(x,y6,'b'),gtext('y6'),pausetitle('曲線擬合0911370132吳坤')2.實驗結(jié)果及作圖三、實驗結(jié)果分析1.輸出多項式：在MATLAB運行窗口輸入>>f2=poly2sym(p2,'x')f2=7816947549294785/1180591620717411303424*x^2-8247092081559201/18446744073709551616*x+4527836499365127/4503599627370496在MATLAB運行窗口輸入>>f3=poly2sym(p3,'x')f3=4767131728475779/151115727451828646838272*x^3+2372191088713079/590295810358705651712*x^2-3569989637372553/9223372036854775808*x+4420227325675/4398046511104在MATLAB運行窗口輸入>>f4=poly2sym(p4,'x')f4=-6396880211016271/1208925819614629174706176*x^4+2897632332185769/4722366482869645213696*x^3-2549950622516187/147573952589676412928*x^2-7086015023430907/73786976294838206464*x+565150149489267/562949953421312在MATLAB運行窗口輸入>>f5=poly2sym(p5,'x')f5=2598880531192617/4835703278458516698824704*x^5-373958587776395/4722366482869645213696*x^4+5112979943580295/1180591620717411303424*x^3-7409227205923235/73786976294838206464*x^2+200547470771097/288230376151711744*x+75113/75000在MATLAB運行窗口輸入>>f6=poly2sym(p6,'x')f6=-971439058605899/19342813113834066795298816*x^6+5333842712335749/604462909807314587353088*x^5-5766170924010877/9444732965739290427392*x^4+774702836934037/36893488147419103232*x^3-209901101886213/576460752303423488*x^2+6059960212873641/2305843009213693952*x+2244166212316849/22517998136852482.誤差分析：>>f2=7816947549294785/1180591620717411303424.*x.^2-8247092081559201/18446744073709551616.*x+4527836499365127/4503599627370496;>>fy2=abs(f2-y);fy22=fy2.^2;E2=sqrt((sum(fy22))/10)E2=2.718817702048033e-004>>f3=4767131728475779/151115727451828646838272.*x.^3+2372191088713079/590295810358705651712.*x.^2-3569989637372553/9223372036854775808.*x+4420227325675/4398046511104;>>fy3=abs(f3-y);fy32=fy3.^2;E3=sqrt((sum(fy32))/10)E3=2.629007098065654e-004>>f4=-6396880211016271/1208925819614629174706176.*x.^4+2897632332185769/4722366482869645213696.*x.^3-2549950622516187/147573952589676412928.*x.^2-7086015023430907/73786976294838206464.*x+565150149489267/562949953421312;>>fy4=abs(f4-y);fy42=fy4.^2;E4=sqrt((sum(fy42))/10)E4=7.088229680251621e+001>>f5=2598880531192617/4835703278458516698824704.*x.^5-373958587776395/4722366482869645213696.*x.^4+5112979943580295/1180591620717411303424.*x.^3-7409227205923235/73786976294838206464.*x.^2+200547470771097/288230376151711744.*x+75113/75000;>>fy5=abs(f5-y);fy52=fy5.^2;E5=sqrt((sum(fy52))/10)E5=1.705824384231118e-004>>f6=-971439058605899/19342813113834066795298816.*x.^6+5333842712335749/604462909807314587353088.*x.^5-5766170924010877/9444732965739290427392.*x.^4+774702836934037/36893488147419103232.*x.^3-209901101886213/576460752303423488.*x.^2+6059960212873641/2305843009213693952.*x+2244166212316849/2251799813685248;>>fy6=abs(f6-y);fy62=fy6.^2;E6=sqrt((sum(fy62))/10)E6=7.088229680251621e+0013.結(jié)果比較：E2=2.718817702048033e-004E3=2.629007098065654e-004E4=7.088229680251621e+001E5=1.705824384231118e-004E6=7.088229680251621e+0014.得出結(jié)論：n=5時擬合效果最好插值問題數(shù)值實驗實驗要求已知函數(shù)取n+1個基點，，對n=2,4,6,8,10分別做n次插值多項式，并同一坐標系中做出在與進行誤差分析實驗內(nèi)容建立M.flie文件functiony=lag(x0,y0,x)n=length(x0);m=length(x);fori=1:mz=x(i);s=0.0;fork=1:np=1.0;forj=1:nifj~=kp=p*(z-x0(j))/(x0(k)-x0(j));endends=p*y0(k)+s;endy(i)=s;end2．主程序>>m=101;x=-5:10/(m-1):5;y=1./(1+(x.^2)*25);>>z=0*x;plot(x,z,'k',x,y,'g:'),>>gtext('y=1./(1+(x.^2)*25)'),pause>>n=3;x0=-5:10/(n-1):5;y0=1./(1+(x0.^2)*25);>>y1=lag(x0,y0,x);>>holdon>>plot(x,y1,'r'),gtext('n=2'),pause,holdoff>>n=5;x0=-5:10/(n-1):5;y0=1./(1+(x0.^2)*25);>>y2=lag(x0,y0,x);>>holdon>>plot(x,y2,'b'),gtext('n=4'),pause,holdoff>>n=7;x0=-5:10/(n-1):5;y0=1./(1+(x0.^2)*25);>>y3=lag(x0,y0,x);>>holdon>>plot(x,y3,'-'),gtext('n=6'),pause,holdoff>>n=9;x0=-5:10/(n-1):5;y0=1./(1+(x0.^2)*25);>>y4=lag(x0,y0,x);>>holdon>>plot(x,y4,'--'),gtext('n=8'),pause,holdoff>>n=11;x0=-5:10/(n-1):5;y0=1./(1+(x0.^2)*25);>>y5=lag(x0,y0,x);>>holdon>>plot(x,y5,'m'),gtext('n=10'),pause,holdoff>>title('n次拉格朗日插值')三、實驗結(jié)果分析1.函數(shù)圖象比較誤差分析由圖象可知當n=6時插值效果最佳矩陣特征值計算實驗實驗要求1.已知矩陣如下2.討論當x=0.9,1.0,1.1時的全部特征值，并觀察特征值的變化實驗內(nèi)容1.源代碼及具體實現(xiàn)>>A1=[9.1,3.0,3.6,4.0;4.2,5.3,4.7,1.6;3.2,1.7,9.4,0.9;6.1,4.9,3.5,6.2;]A1=9.10003.00003.60004.00004.20005.30004.70001.60003.20001.70009.40000.90006.10004.90003.50006.2000>>Y1=eig(A1)Y1=17.69696.67562.8137+0.6630i2.8137-0.6630i>>A2=[9.1,3.0,3.6,4.0;4.2,5.3,4.7,1.6;3.2,1.7,9.4,1.0;6.1,4.9,3.5,6.2;]A2=9.10003.00003.60004.00004.20005.30004.70001.60003.20001.70009.40001.00006.10004.90003.50006.2000>>Y2=eig(A2)Y2=17.73606.62942.8173+0.7029i2.8173-0.7029i>>A3=[9.1,3.0,3.6,4.0;4.2,5.3,4.7,1.6;3.2,1.7,9.4,1.1;6.1,4.9,3.5,6.2;]A3=9.10003.00003.60004.00004.20005.30004.70001.60003.20001.70009.40001.10006.10004.90003.50006.2000>>Y3=eig(A3)Y3=17.77476.58362.8208+0.7413i2.8208-0.7413i>>A4=[9.1,3.0,3.6,4.0;4.2,5.3,4.7,1.6;3.2,1.7,9.4,1.5;6.1,4.9,3.5,6.2;]A4=9.10003.00003.60004.00004.20005.30004.70001.60003.20001.70009.40001.50006.10004.90003.50006.2000>>Y4=eig(A4)Y4=17.92686.40562.8338+0.8842i2.8338-0.8842i>>A5=[9.1,3.0,3.6,4.0;4.2,5.3,4.7,1.6;3.2,1.7,9.4,3;6.1,4.9,3.5,6.2;]A5=9.10003.00003.60004.00004.20005.30004.70001.60003.20001.70009.40003.00006.10004.90003.50006.2000>>Y5=eig(A5)Y5=18.46105.81922.8599+1.3473i2.8599-1.3473i>>A6=[9.1,3.0,3.6,4.0;4.2,5.3,4.7,1.6;3.2,1.7,9.4,6;6.1,4.9,3.5,6.2;]A6=9.10003.00003.60004.00004.20005.30004.70001.60003.20001.70009.40006.00006.10004.90003.50006.2000>>Y6=eig(A6)Y6=19.40045.09172.7539+2.1295i2.7539-2.1295i三、實驗結(jié)果分析X=0.9Y1=17.69696.67562.8137+0.6630i2.8137-0.6630iX=1.0Y2=17.73606.62942.8173+0.7029i2.8173-0.7029iX=1.1Y3=17.77476.58362.8208+0.7413i2.8208-0.7413iX=1.5Y4=17.92686.40562.8338+0.8842i2.8338-0.8842iX=3.0Y5=18.46105.81922.8599+1.3473i2.8599-1.3473iX=6.0Y6=19.40045.09172.7539+2.1295i2.7539-2.1295i2.結(jié)果分析由以上結(jié)果可以看出，四個解中，隨著x增大，兩個實數(shù)解一個增大，一個減?。粌蓚€復數(shù)解實部、虛部絕對值都增大，即復數(shù)的模增大常微分方程初值問題實驗一、實驗要求下面的病態(tài)例子是由達爾奎斯特和比約克1974年給出的?？紤]帶初值x（0）=0的微分方程x’=100（sint-x），在區(qū)間[0,3]上用標準四階Runge-Kutta法解決這個問題，分別取h=0.015,0.020,0.025和0.030，觀察數(shù)值的不穩(wěn)定性。二、實驗內(nèi)容（1）Runge-Kutta公式在MATLAB的實現(xiàn)functionR=rk(f,a,b,ya,N)h=(b-a)/NT=zeros(1,N+1);Y=zeros(1,N+1);T=a:h:b;Y(1)=ya;forj=1:Nk1=h*feval(f,T(j),Y(j));k2=h*feval(f,T(j)+h/2,Y(j)+k1/2);k3=h*feval(f,T(j)+h/2,Y(j)+k2/2);k4=h*feval(f,T(j)+h,Y(j)+k3);Y(j+1)=Y(j)+(k1+2*k2+2*k3+k4)/6;endR=[T'Y']（2）建立一個M-文件，其內(nèi)容為functionz=f(t,x)z=100*[sin(t)-x];考慮到要研究的h值，N=3/h當h=0.015時，取N=3/0.015在MATLAB運行窗口輸入>>rk('f',0,3,0,200)輸出結(jié)果為R=000.01500.00770.03000.02070.04500.03520.06000.05000.07500.06500.09000.07990.10500.09490.12000.10980.13500.12470.15000.13950.16500.15440.18000.16920.19500.18390.21000.19870.22500.21330.24000.22800.25500.24250.27000.25710.28500.27150.30000.28590.31500.30030.33000.31450.34500.32870.36000.34290.37500.35690.39000.37090.40500.38480.42000.39860.43500.41230.45000.42590.46500.43940.48000.45290.49500.46620.51000.47940.52500.49250.54000.50550.55500.51840.57000.53120.58500.54380.60000.55630.61500.56870.63000.58100.64500.59310.66000.60510.67500.61700.69000.62880.70500.64030.72000.65180.73500.66310.75000.67420.76500.68520.78000.69610.79500.70680.81000.71730.82500.72770.84000.73790.85500.74790.87000.75780.88500.76750.90000.77700.91500.78640.93000.79560.94500.80460.96000.81340.97500.82200.99000.83041.00500.83871.02000.84681.03500.85471.05000.86241.06500.86981.08000.87711.09500.88421.11000.89121.12500.89791.14000.90441.15500.91071.17000.91671.18500.92261.20000.92831.21500.93381.23000.93901.24500.94411.26000.94891.27500.95351.29000.95801.30500.96221.32000.96611.33500.96991.35000.97341.36500.97671.38000.97981.39500.98271.41000.98541.42500.98781.44000.99001.45500.99201.47000.99381.48500.99541.50000.99671.51500.99781.53000.99861.54500.99931.56000.99971.57500.99991.59000.99991.60500.99961.62000.99921.63500.99851.65000.99751.66500.99641.68000.99501.69500.99341.71000.99161.72500.98961.74000.98731.75500.98481.77000.98211.78500.97921.80000.97601.81500.97261.83000.96911.84500.96521.86000.96121.87500.95701.89000.95251.90500.94781.92000.94301.93500.93791.95000.93261.96500.92701.98000.92131.99500.91542.01000.90922.02500.90292.04000.89642.05500.88962.07000.88272.08500.87552.10000.86822.11500.86062.13000.85292.14500.84502.16000.83682.17500.82852.19000.82012.20500.81142.22000.80252.23500.79352.25000.78432.26500.77492.28000.76532.29500.75562.31000.74572.32500.73562.34000.72532.35500.71492.37000.70442.38500.69362.40000.68282.41500.67172.43000.66052.44500.64922.46000.63772.47500.62612.49000.61432.50500.60242.52000.59042.53500.57822.55000.56592.56500.55352.58000.54092.59500.52832.61000.51552.62500.50262.64000.48952.65500.47642.67000.46322.68500.44982.70000.43642.71500.42282.73000.40922.74500.39552.76000.38162.77500.36772.79000.35372.80500.33972.82000.32552.83500.31132.85000.29702.86500.28272.88000.26822.89500.25382.91000.23922.92500.22462.94000.21002.95500.19532.97000.18062.98500.16583.00000.1510ans=000.01500.00770.03000.02070.04500.03520.06000.05000.07500.06500.09000.07990.10500.09490.12000.10980.13500.12470.15000.13950.16500.15440.18000.16920.19500.18390.21000.19870.22500.21330.24000.22800.25500.24250.27000.25710.28500.27150.30000.28590.31500.30030.33000.31450.34500.32870.36000.34290.37500.35690.39000.37090.40500.38480.42000.39860.43500.41230.45000.42590.46500.43940.48000.45290.49500.46620.51000.47940.52500.49250.54000.50550.55500.51840.57000.53120.58500.54380.60000.55630.61500.56870.63000.58100.64500.59310.66000.60510.67500.61700.69000.62880.70500.64030.72000.65180.73500.66310.75000.67420.76500.68520.78000.69610.79500.70680.81000.71730.82500.72770.84000.73790.85500.74790.87000.75780.88500.76750.90000.77700.91500.78640.93000.79560.94500.80460.96000.81340.97500.82200.99000.83041.00500.83871.02000.84681.03500.85471.05000.86241.06500.86981.08000.87711.09500.88421.11000.89121.12500.89791.14000.90441.15500.91071.17000.91671.18500.92261.20000.92831.21500.93381.23000.93901.24500.94411.26000.94891.27500.95351.29000.95801.30500.96221.32000.96611.33500.96991.35000.97341.36500.97671.38000.97981.39500.98271.41000.98541.42500.98781.44000.99001.45500.99201.47000.99381.48500.99541.50000.99671.51500.99781.53000.99861.54500.99931.56000.99971.57500.99991.59000.99991.60500.99961.62000.99921.63500.99851.65000.99751.66500.99641.68000.99501.69500.99341.71000.99161.72500.98961.74000.98731.75500.98481.77000.98211.78500.97921.80000.97601.81500.97261.83000.96911.84500.96521.86000.96121.87500.95701.89000.95251.90500.94781.92000.94301.93500.93791.95000.93261.96500.92701.98000.92131.99500.91542.01000.90922.02500.90292.04000.89642.05500.88962.07000.88272.08500.87552.10000.86822.11500.86062.13000.85292.14500.84502.16000.83682.17500.82852.19000.82012.20500.81142.22000.80252.23500.79352.25000.78432.26500.77492.28000.76532.29500.75562.31000.74572.32500.73562.34000.72532.35500.71492.37000.70442.38500.69362.40000.68282.41500.67172.43000.66052.44500.64922.46000.63772.47500.62612.49000.61432.50500.60242.52000.59042.53500.57822.55000.56592.56500.55352.58000.54092.59500.52832.61000.51552.62500.50262.64000.48952.65500.47642.67000.46322.68500.44982.70000.43642.71500.42282.73000.40922.74500.39552.76000.38162.77500.36772.79000.35372.80500.33972.82000.32552.83500.31132.85000.29702.86500.28272.88000.26822.89500.25382.91000.23922.92500.22462.94000.21002.95500.19532.97000.18062.98500.16583.00000.1510當h=0.020時，取N=3/0.020在MATLAB運行窗口輸入>>rk('f',0,3,0,150)R=000.02000.01330.04000.03110.06000.05030.08000.07010.10000.08990.12000.10980.14000.12960.16000.14940.18000.16920.20000.18880.22000.20840.24000.22800.26000.24740.28000.26670.30000.28590.32000.30500.34000.32400.36000.34290.38000.36160.40000.38020.42000.39860.44000.41680.46000.43490.48000.45280.50000.47060.52000.48810.54000.50550.56000.52260.58000.53960.60000.55630.62000.57280.64000.58910.66000.60510.68000.62090.70000.63650.72000.65180.74000.66680.76000.68160.78000.69610.80000.71030.82000.72420.84000.73790.86000.75120.88000.76430.90000.77700.92000.78940.94000.80150.96000.81330.98000.82481.00000.83591.02000.84671.04000.85721.06000.86731.08000.87711.10000.88651.12000.89561.14000.90431.16000.91271.18000.92071.20000.92831.22000.93551.24000.94241.26000.94891.28000.95501.30000.96071.32000.96611.34000.97111.36000.97561.38000.97981.40000.98361.42000.98701.44000.99001.46000.99261.48000.99481.50000.99661.52000.99811.54000.99911.56000.99971.58000.99991.60000.99971.62000.99911.64000.99811.66000.99681.68000.99501.70000.99281.72000.99021.74000.98731.76000.98391.78000.98011.80000.97601.82000.97141.84000.96651.86000.96121.88000.95551.90000.94941.92000.94291.94000.93611.96000.92891.98000.92132.00000.91332.02000.90502.04000.89632.06000.88732.08000.87792.10000.86812.12000.85802.14000.84762.16000.83682.18000.82572.20000.81432.22000.80252.24000.79042.26000.77802.28000.76532.30000.75232.32000.73892.34000.72532.36000.71142.38000.69722.40000.68272.42000.66802.44000.65302.46000.63772.48000.62222.50000.60642.52000.59042.54000.57412.56000.55762.58000.54092.60000.52402.62000.50692.64000.48952.66000.47202.68000.45432.70000.43642.72000.41832.74000.40002.76000.38162.78000.36312.80000.34442.82000.32552.84000.30652.86000.28742.88000.26822.90000.24892.92000.22952.94000.21002.96000.19042.98000.17073.00000.1510ans=000.02000.01330.04000.03110.06000.05030.08000.07010.10000.08990.12000.10980.14000.12960.16000.14940.18000.16920.20000.18880.22000.20840.24000.22800.26000.24740.28000.26670.30000.28590.32000.30500.34000.32400.36000.34290.38000.36160.40000.38020.42000.39860.44000.41680.46000.43490.48000.45280.50000.47060.52000.48810.54000.50550.56000.52260.58000.53960.60000.55630.62000.57280.64000.58910.66000.60510.68000.62090.70000.63650.72000.65180.74000.66680.76000.68160.78000.69610.80000.71030.82000.72420.84000.73790.86000.75120.88000.76430.90000.77700.92000.78940.94000.80150.96000.81330.98000.82481.00000.83591.02000.84671.04000.85721.06000.86731.08000.87711.10000.88651.12000.89561.14000.90431.16000.91271.18000.92071.20000.92831.22000.93551.24000.94241.26000.94891.28000.95501.30000.96071.32000.96611.34000.97111.36000.97561.38000.97981.40000.98361.42000.98701.44000.99001.46000.99261.48000.99481.50000.99661.52000.99811.54000.99911.56000.99971.58000.99991.60000.99971.62000.99911.64000.99811.66000.99681.68000.99501.70000.99281.72000.99021.74000.98731.76000.98391.78000.98011.80000.97601.82000.97141.84000.96651.86000.96121.88000.95551.90000.94941.92000.94291.94000.93611.96000.92891.98000.92132.00000.91332.02000.90502.04000.89632.06000.88732.08000.87792.10000.86812.12000.85802.14000.84762.16000.83682.18000.82572.20000.81432.22000.80252.24000.79042.26000.77802.28000.76532.30000.75232.32000.73892.34000.72532.36000.71142.38000.69722.40000.68272.42000.66802.44000.65302.46000.63772.48000.62222.50000.60642.52000.59042.54000.57412.56000.55762.58000.54092.60000.52402.62000.50692.64000.48952.66000.47202.68000.45432.70000.43642.72000.41832.74000.40002.76000.38162.78000.36312.80000.34442.82000.32552.84000.30652.86000.28742.88000.26822.90000.24892.92000.22952.94000.21002.96000.19042.98000.17073.00000.1510當h=0.025時，取N=3/0.025在MATLAB運行窗口輸入>>rk('f',0,3,0,120)R=000.02500.02150.05000.04420.07500.06770.10000.09160.12500.11590.15000.14030.17500.16470.20000.18910.22500.21350.25000.23780.27500.26190.30000.28590.32500.30980.35000.33340.37500.35690.40000.38010.42500.40310.45000.42580.47500.44830.50000.47050.52500.49240.55000.51400.57500.53530.60000.55620.62500.57680.65000.59700.67500.61690.70000.63630.72500.65540.75000.67410.77500.69230.80000.71010.82500.72750.85000.74440.87500.76080.90000.77680.92500.79230.95000.80730.97500.82181.00000.83581.02500.84921.05000.86211.07500.87451.10000.88631.12500.89761.15000.90831.17500.91851.20000.92811.22500.93711.25000.94551.27500.95331.30000.96051.32500.96711.35000.97321.37500.97861.40000.98341.42500.98761.45000.99111.47500.99411.50000.99641.52500.99811.55000.99921.57500.99961.60000.99951.62500.99871.65000.99731.67500.99521.70000.99261.72500.98931.75000.98541.77500.98091.80000.97571.82500.97001.85000.96371.87500.95671.90000.94921.92500.94101.95000.93231.97500.92302.00000.91312.02500.90262.05000.89162.07500.88002.10000.86792.12500.85522.15000.84202.17500.82832.20000.81412.22500.79932.25000.78402.27500.76832.30000.75212.32500.73542.35000.71822.37500.70062.40000.68262.42500.66412.45000.64522.47500.62592.50000.60622.52500.58622.55000.56572.57500.54502.60000.52392.62500.50242.65000.48062.67500.45862.70000.43622.72500.41362.75000.39072.77500.36762.80000.34432.82500.32072.85000.29692.87500.27302.90000.24882.92500.22462.95000.20012.97500.17563.00000.1509ans=000.02500.02150.05000.04420.07500.06770.10000.09160.12500.11590.15000.14030.17500.16470.20000.18910.22500.21350.25000.23780.27500.26190.30000.28590.32500.30980.35000.33340.37500.35690.40000.38010.42500.40310.45000.42580.47500.44830.50000.47050.52500.49240.55000.51400.57500.53530.60000.55620.62500.57680.65000.59700.67500.61690.70000.63630.72500.65540.75000.67410.77500.69230.80000.71010.82500.72750.85000.74440.87500.76080.90000.77680.92500.79230.95000.80730.97500.82181.00000.83581.02500.84921.05000.86211.07500.87451.10000.88631.12500.89761.15000.90831.17500.91851.20000.92811.22500.93711.25000.94551.27500.95331.30000.96051.32500.96711.35000.97321.37500.97861.40000.98341.42500.98761.45000.99111.47500.99411.50000.99641.52500.99811.55000.99921.57500.99961.60000.99951.62500.99871.65000.99731.67500.99521.70000.99261.72500.98931.75000.98541.77500.98091.80000.97571.82500.97001.85000.96371.87500.95671.90000.94921.92500.94101.95000.93231.97500.92302.00000.91312.02500.90262.05000.89162.07500.88002.10000.86792.12500.85522.15000.84202.17500.82832.20000.81412.22500.79932.25000.78402.27500.76832.30000.75212.32500.73542.35000.71822.37500.70062.40000.68262.42500.66412.45000.64522.47500.62592.50000.60622.52500.58622.55000.56572.57500.54502.60000.52392.62500.50242.65000.48062.67500.45862.70000.43622.72500.41362.75000.39072.77500.36762.80000.34432.82500.32072.85000.29692.87500.27302.90000.24882.92500.22462.95000.20012.97500.17563.00000.1509當h=0.030時，取N=3/0.030在MATLAB運行窗口輸入>>rk('f',0,3,0,100)R