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1、MATLAB程序设计实验6解方程和最优化问题求解一．实验目的1.掌握线性方程组的数值求解方法。2.掌握常微分方程的数值求解方法。3.掌握非线性方程以及最优化问题的求解方法。二．实验内容1.对下列线性病态方程组：a)求方程组的解。>>A=[1/2,1/3,1/4;1/3,1/4,1/5;1/4,1/5,1/6];>>b=[0.95,0.67,0.52]';>>x=Abx=1.20000.60000.6000b)将方程组右边的向量元素b3（0.52）修改为0.53，再次求方程组的解。比较b3的变化和解的相对变化。
2、>>A=[1/2,1/3,1/4;1/3,1/4,1/5;1/4,1/5,1/6];b=[0.95,0.67,0.53]';x=Abx=3.0000-6.60006.6000c)求系数矩阵的条件数，并分析条件数对线性方程组求解的影响。2.求方程的解。a)函数文件：funx.mfunctionfx=funx(x)fx=x^41+x^3+1;调用：>>z=fzero(@funx,-1)z=-0.9525a)函数文件funx.mfunctionfx=funx(x)fx=x-sin(x)./x;>>z=fzero(@
3、funx,0.5)z=0.8767c)，函数文件：funx.m>>z=fzero(@funx,0.5)z=0.8767调用函数：>>options=optimset('Display','off');>>x=fsolve(@funx,[1,1,1]',options)x=0.59912.39592.00502.求常微分方程的数值解。a)，函数文件：functionyp=funx(t,y)yp=-(1.2+sin(10*t)).*y;函数调用：>>t0=0;>>tf=5;>>y0=1;>>[t,y]=ode23(
4、@funx,[t0,tf],y0);>>t'ans=Columns1through900.06670.13750.20030.26950.35280.43620.50330.5663Columns10through180.63690.69130.74570.80810.87380.95911.02771.09631.1600Columns19through271.22461.30821.37141.43471.50011.58421.65301.72191.7858Columns28through361.850
5、11.93191.99532.05872.12362.20532.27452.34382.4080Columns37through452.47192.55012.61402.67792.74192.81932.90462.96853.0323Columns46through543.09593.17213.23643.30073.36423.43953.53283.59653.6602Columns55through633.72383.79983.86423.92863.99204.06714.14084.214
6、44.2800Columns64through724.34324.41594.48124.54654.60944.68124.75674.83224.8990Columns73through744.96205.0000>>y'ans=Columns1through91.00000.90350.78220.68230.59840.54020.51820.51060.4976Columns10through180.46560.42800.38440.33550.29360.25950.24690.24210.238
7、2Columns19through270.22900.20540.18190.15850.13870.12250.11640.11400.1122Columns28through360.10800.09740.08640.07530.06580.05810.05490.05370.0529Columns37through450.05110.04660.04150.03610.03160.02780.02580.02530.0249Columns46through540.02410.02210.01970.017
8、20.01500.01320.01220.01190.0117Columns55through630.01140.01040.00930.00810.00710.00620.00580.00560.0055Columns64through720.00540.00500.00450.00390.00340.00300.00270.00260.0026Columns73through740
