MATLAB实验十一

实验十一、线性代数中的数值计算问题

1、>> f(1)=1;f(2)=0;f(3)=1;for n=4:100,f(n)=f(n-1)-2*f(n-2)+f(n-3);end 求最大值：

>> max=0;for i=1:100,if f(i)>max max=f(i);end,end,max max =

4.3776e+011 求最小值：

>> min=max;for j=1:100,if f(i)

-8.9941e+011 各数之和：

>> s=0;for k=1:100,s=s+f(i);end,s s =

-8.9941e+013

正数 零 负数的个数：

>> zhengshu=0;fushu=0;ling=0;for i=1:100,if (f(i)>0)

zhengshu=zhengshu+1;elseif(f(i)==0) ling=ling+1;else fushu=fushu+1;end,end >> zhengshu zhengshu = 49 >> fushu fushu = 49 >> ling ling = 2

2、假设有一组数据，分别绘制1-4次及10-13次拟合曲线。 1-4次拟合：

>> x=0.1:0.1:1;y=[2.3201 2.6470 2.9070 3.2885 3.6008 3.9090 4.2147 4.5191 4.8232 5.1275];xi=linspace(0,1);yil=polyval(a1,xi);subplot(2,2,1),plot(x,y,'o',xi,yil,'b'),subplot(2,2,2),a2=polyfit(x,y,2);yi2=polyval(a2,xi);plot(x,y,'o',xi,yi2,'m'),subplot(2,2,3),a3=polyfit(x,y,3);yi3=polyval(a3,xi);plot(x,y,'o',xi,yi3,'r'),subplot(2,2,4),a4=polyfit(x,y,4);yi4=polyval(a4,xi);plot(x,y,'o',xi,yi4,'c')

1

10-13次拟合：

>> subplot(2,2,1),a10=polyfit(x,y,10);yi10=polyval(a10,xi);plot(x,y,'o',xi,yi10,'m'), subplot(2,2,2),a11=polyfit(x,y,11);yi11=polyval(a11,xi);plot(x,y,'o',xi,yi11,'m'), subplot(2,2,3),a13=polyfit(x,y,13);yi13=polyval(a13,xi);plot(x,y,'o',xi,yi13,'m'), subplot(2,2,4),a14=polyfit(x,y,14);yi14=polyval(a14,xi);plot(x,y,'o',xi,yi14,'m')

3、求多项式的根

>> a=[3 4 7 2 9 12];gen=roots(a) gen =

-0.8612 + 1.4377i -0.8612 - 1.4377i 0.6737 + 1.0159i 0.6737 - 1.0159i -0.9583

4、把1开五次方，求其五个根 >> b=[1 0 0 0 0 -1];roots(b) ans =

-0.8090 + 0.5878i -0.8090 - 0.5878i 0.3090 + 0.9511i 0.3090 - 0.9511i 1.0000

5、设方程的根为x=[-3 -5 -8 -9],求他们的x多项式的系数 >> x=[-3 -5 -8 -9];xishu=poly(x) xishu =

1 25 223 831 6、脉冲

b=[1 0];a=[1 2 5 4 0 3];[r,p,k]=residue(b,a) r =

0.0128 + 0.0558i 0.0128 - 0.0558i -0.0981 0.0363 - 0.0610i 0.0363 + 0.0610i

2

1080 p =

-0.5835 + 1.9707i -0.5835 - 1.9707i -1.3608 0.2639 + 0.6725i 0.2639 - 0.6725i k =

[]

>>t=0:0.1:10;yi=r(1)*exp(p(1)*t)+r(2)*exp(p(2)*t)+r(3)*exp(p(3)*t);plot(t,yi) 阶跃

>> b=[1 0];a=[1 2 5 4 0 3 0];[r,p,k]=residue(b,a) r =

0.0243 - 0.0137i 0.0243 + 0.0137i 0.0721 -0.0603 - 0.0776i -0.0603 + 0.0776i 0 p =

-0.5835 + 1.9707i -0.5835 - 1.9707i -1.3608 0.2639 + 0.6725i 0.2639 - 0.6725i 0 k =

[]

>> t=0:0.1:10;ys=r(1)*exp(p(1)*t)+r(2)*exp(p(2)*t)+r(3)*exp(p(3)*t)+r(4);plot(t,ys) 7、

R1=randn(4,6) R1 =

-0.6918 -1.4410 0.8156 1.1908 -1.6041 -0.8051 0.8580 0.5711 0.7119 -1.2025 0.2573 0.5287 1.2540 -0.3999 1.2902 -0.0198 -1.0565 0.2193 -1.5937 0.6900 0.6686 -0.1567 1.4151 -0.9219 >> m=mean(R1),s=std(R1) m =

-0.0434 -0.1449 0.8716 -0.0470 -0.2470 -0.2447 s =

1.3316 0.9924 0.2858 0.9798 1.3557 0.7271

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