MATLAB第二次上机实验报告

电子科技大学电子工程学院标准实验报告（实验）课程名称MATLAB与数值分析学生姓名：学号：指导教师：实验名称实验二线性方程组求解和函数的数值逼近实验目的通过上机实验，使学生对病态问题、线性方程组求解和函数的数值逼近方法有一个初步的理解。实验涉及的核心知识点：病态方程求解、矩阵分解和方程组求解、Lagrange插值。实验重点与难点：算法设计和MATLAB编程实验内容1.对高阶多项式编程求下面方程的解并绘图演示方程的解与扰动量的关系。2.对，生成对应的Hilbert矩阵，计算矩阵的条件数；通过先确定解获得常向量b的方法，确定方程组最后，用矩阵分解方法求解方程组，并分析计算结果。3.对函数的Chebyshev点，编程进行Lagrange插值，并分析插值结果。实验数据及结果分析对高阶多项式编程求下面方程的解并绘图演示方程的解与扰动量的关系。p=[1,-1];fori=2:20n=[1,-i];p=conv(p,n);%求多项式乘积endm=zeros(1,21);%m的最高次幂为20，有21项holdonx=1:20;d=[-1,0,0.1,0.5,1];fori=1:5delt=d(i);m(2)=delt;y=(roots(p+m))';%求多项式的根plot(x,y,'-o','color',[i/5,i/20,i/10]);endtitle('方程p(x)=0的解与扰动量delt的关系')legend('delt=-1','delt=0','delt=0.1','delt=0.5','delt=1')2.对，生成对应的Hilbert矩阵，计算矩阵的条件数；通过先确定解获得常向量b的方法，确定方程组最后，用矩阵分解方法求解方程组，并分析计算结果。forn=2:20h=hilb(n);fprintf('\n\nn=%-10dcond(Hn)∞=%d',n,cond(h,'inf'))%cond：求矩阵范数X=1:n;b=h*X';[lu]=lu(h);%lu分解x=u\(l\b);%利用lu分解求线性其次方程组的根x=x';fprintf('\nX’=')fori=1:nfprintf('%-8.2f',X(i))endfprintf('\nx’=')fori=1:nfprintf('%-8.2f',x(i))endend输出结果如下：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.对函数的Chebyshev点，编程进行Lagrange插值，并分析插值结果。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