MATLAB第二次上機(jī)實(shí)驗(yàn)報(bào)告

電子科技大學(xué)電子工程學(xué)院標(biāo)準(zhǔn)實(shí)驗(yàn)報(bào)告（實(shí)驗(yàn)）課程名稱MATLAB與數(shù)值分析學(xué)生姓名：學(xué)號(hào)：指導(dǎo)教師：實(shí)驗(yàn)名稱實(shí)驗(yàn)二線性方程組求解和函數(shù)的數(shù)值逼近實(shí)驗(yàn)?zāi)康耐ㄟ^(guò)上機(jī)實(shí)驗(yàn)，使學(xué)生對(duì)病態(tài)問(wèn)題、線性方程組求解和函數(shù)的數(shù)值逼近方法有一個(gè)初步的理解。實(shí)驗(yàn)涉及的核心知識(shí)點(diǎn)：病態(tài)方程求解、矩陣分解和方程組求解、Lagrange插值。實(shí)驗(yàn)重點(diǎn)與難點(diǎn)：算法設(shè)計(jì)和MATLAB編程實(shí)驗(yàn)內(nèi)容1.對(duì)高階多項(xiàng)式編程求下面方程的解并繪圖演示方程的解與擾動(dòng)量的關(guān)系。2.對(duì)，生成對(duì)應(yīng)的Hilbert矩陣，計(jì)算矩陣的條件數(shù)；通過(guò)先確定解獲得常向量b的方法，確定方程組最后，用矩陣分解方法求解方程組，并分析計(jì)算結(jié)果。3.對(duì)函數(shù)的Chebyshev點(diǎn)，編程進(jìn)行Lagrange插值，并分析插值結(jié)果。實(shí)驗(yàn)數(shù)據(jù)及結(jié)果分析對(duì)高階多項(xiàng)式編程求下面方程的解并繪圖演示方程的解與擾動(dòng)量的關(guān)系。p=[1,-1];fori=2:20n=[1,-i];p=conv(p,n);%求多項(xiàng)式乘積endm=zeros(1,21);%m的最高次冪為20，有21項(xiàng)holdonx=1:20;d=[-1,0,0.1,0.5,1];fori=1:5delt=d(i);m(2)=delt;y=(roots(p+m))';%求多項(xiàng)式的根plot(x,y,'-o','color',[i/5,i/20,i/10]);endtitle('方程p(x)=0的解與擾動(dòng)量delt的關(guān)系')legend('delt=-1','delt=0','delt=0.1','delt=0.5','delt=1')2.對(duì)，生成對(duì)應(yīng)的Hilbert矩陣，計(jì)算矩陣的條件數(shù)；通過(guò)先確定解獲得常向量b的方法，確定方程組最后，用矩陣分解方法求解方程組，并分析計(jì)算結(jié)果。forn=2:20h=hilb(n);fprintf('\n\nn=%-10dcond(Hn)∞=%d',n,cond(h,'inf'))%cond：求矩陣范數(shù)X=1:n;b=h*X';[lu]=lu(h);%lu分解x=u\(l\b);%利用lu分解求線性其次方程組的根x=x';fprintf('\nX’=')fori=1:nfprintf('%-8.2f',X(i))endfprintf('\nx’=')fori=1:nfprintf('%-8.2f',x(i))endend輸出結(jié)果如下：n=2cond(Hn)∞=2.700000e+001X’=1.002.00x’=1.002.00n=3cond(Hn)∞=7.480000e+002X’=1.002.003.00x’=1.002.003.00n=4cond(Hn)∞=2.837500e+004X’=1.002.003.004.00x’=1.002.003.004.00n=5cond(Hn)∞=9.436560e+005X’=1.002.003.004.005.00x’=1.002.003.004.005.00n=6cond(Hn)∞=2.907028e+007X’=1.002.003.004.005.006.00x’=1.002.003.004.005.006.00n=7cond(Hn)∞=9.851949e+008X’=1.002.003.004.005.006.007.00x’=1.002.003.004.005.006.007.00n=8cond(Hn)∞=3.387279e+010X’=1.002.003.004.005.006.007.008.00x’=1.002.003.004.005.006.007.008.00n=9cond(Hn)∞=1.099652e+012X’=1.002.003.004.005.006.007.008.009.00x’=1.002.003.004.005.006.007.008.009.00n=10cond(Hn)∞=3.535369e+013X’=1.002.003.004.005.006.007.008.009.0010.00x’=1.002.003.004.005.006.007.008.009.0010.00n=11cond(Hn)∞=1.229476e+015X’=1.002.003.004.005.006.007.008.009.0010.0011.00x’=1.002.003.004.005.006.007.017.999.0110.0011.00Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=2.692153e-017.>Incondat48InUntitled7at3n=12cond(Hn)∞=3.714499e+016X’=1.002.003.004.005.006.007.008.009.0010.0011.0012.00x’=1.002.003.004.005.035.877.347.389.729.4811.2211.96Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=2.739612e-018.>Incondat48InUntitled7at3n=13cond(Hn)∞=3.650152e+017X’=1.002.003.004.005.006.007.008.009.0010.0011.0012.0013.00x’=1.002.003.004.064.508.73-2.5630.28-25.8446.13-12.8421.0611.49Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=2.448199e-019.>Incondat48InUntitled7at3n=14cond(Hn)∞=4.084635e+018Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=4.455948e-017.>InUntitled7at7X’=1.002.003.004.005.006.007.008.009.0010.0011.0012.0013.0014.00x’=1.002.002.974.442.0315.85-1.01-51.32265.98-505.38620.05-421.65185.67-15.62Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=1.024999e-018.>Incondat48InUntitled7at3n=15cond(Hn)∞=9.756108e+017X’=1.002.003.004.005.006.007.008.009.0010.0011.0012.0013.0014.0015.00x’=1.002.003.004.064.468.92-2.4825.120.44-24.72105.39-105.0395.41-17.8220.26Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=9.721674e-019.>Incondat48InUntitled7at3n=16cond(Hn)∞=1.028629e+018Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=7.948463e-017.>InUntitled7at7X’=1.002.003.004.005.006.007.008.009.0010.0011.0012.0013.0014.0015.0016.00x’=1.002.003.004.034.727.621.0721.31-5.460.6173.43-98.66124.04-53.4038.1712.52Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=1.305919e-018.>Incondat48InUntitled7at3n=17cond(Hn)∞=1.038063e+018Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=1.798429e-016.>InUntitled7at7X’=1.002.003.004.005.006.007.008.009.0010.0011.0012.0013.0014.0015.0016.0017.00x’=1.002.002.994.104.1310.17-4.8226.200.84-8.4939.866.132.665.8041.30-2.0621.18Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=1.076656e-019.>Incondat48InUntitled7at3n=18cond(Hn)∞=9.288018e+018Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=7.626119e-018.>InUntitled7at7X’=1.002.003.004.005.006.007.008.009.0010.0011.0012.0013.0014.0015.0016.0017.0018.00x’=1.002.003.013.807.66-12.7283.21-172.57233.93-71.26-41.44-156.96387.29200.16-1079.371233.14-583.42133.55Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=1.592243e-019.>Incondat48InUntitled7at3n=19cond(Hn)∞=6.280448e+018Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=6.040620e-017.>InUntitled7at7X’=1.002.003.004.005.006.007.008.009.0010.0011.0012.0013.0014.0015.0016.0017.0018.0019.00x’=1.002.003.003.876.72-6.0456.65-114.38178.86-96.3643.65-153.15318.1462.48-704.50954.66-554.42187.88-0.06Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=1.155429e-019.>Incondat48InUntitled7at3n=20cond(Hn)∞=8.654794e+018Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=5.444860e-017.>InUntitled7at7X’=1.002.003.004.005.006.007.008.009.0010.0011.0012.0013.0014.0015.0016.0017.0018.0019.0020.00x’=1.002.002.984.332.1719.67-30.0954.4225.37-114.26123.0054.10-75.28-8.2077.82-85.30307.17-360.30236.32-26.913.對(duì)函數(shù)的Chebyshev點(diǎn)，編程進(jìn)行Lagrange插值，并分析插值結(jié)果。functiony=lagrangen(x0,y0,x)n=length(x0);m=length(x);fori=1:mz=x(i);s=0;fork=1:nL=1;forj=1:nifj~=kL=L*(z-x0(j))/(x0(k)-x0(j));endends=s+L*y0(k);e