数值分析matlab作业.doc

目录第一章2第1题2第3题2第4题：3第二章6第1题6第2题7第4题8第三章11第1题11第五章13第1题13第七章16第1题：16第八章18第1题18第一章第1题程序：format long i=1; y1=sqrt(5);y2=sqrt(y1); while y1-y210-8 y1=5.(1./(2.i);y2=5.(1./(2.(i+1); i=i+1;endy1,y2,i运行结果：y1 = 1.000000011991247y2 = 1.000000005995624i =28第3题程序：x=-pi:0.01:pi;y=sin(x); y2=x;y5=x;y10=x;for i=1:2 y2=(-1)i.*(x.(2*i+1)./(factorial(2*i+1)+y2;endfor i=1:5 y5=(-1)i.*(x.(2*i+1)./(factorial(2*i+1)+y5;endfor i=1:10 y10=(-1)i.*(x.(2*i+1)./(factorial(2*i+1)+y10;endplot(x,y,-b,x,y2,-g,x,y5,:r,x,y10,:k);legend(y,y2,y5,y10)运行结果：第4题：程序：等分100份x=-10:0.2:10;y=-10:0.2:10;x,y=meshgrid(x,y); z=exp(-abs(x)+cos(x+y)+1./(x.2+y.2+1);z=exp(-abs(x)+cos(x+y)+1./(x.2+y.2+1);mesh(x,y,z)运行结果：等分200份x=-10:0.1:10;y=-10:0.1:10;x,y=meshgrid(x,y); z=exp(-abs(x)+cos(x+y)+1./(x.2+y.2+1);z=exp(-abs(x)+cos(x+y)+1./(x.2+y.2+1);mesh(x,y,z)运行结果：等分300份x=-10:0.05:10;y=-10:0.05:10;x,y=meshgrid(x,y); z=exp(-abs(x)+cos(x+y)+1./(x.2+y.2+1);z=exp(-abs(x)+cos(x+y)+1./(x.2+y.2+1);mesh(x,y,z)运行结果：第二章第1题程序：列主元素求解A=1 1 1 1 1;1 2 3 4 5;1 3 6 10 15;1 4 10 20 35;1 5 15 35 70;L,U,P=lu(A)L = 1.0000 0 0 0 0 1.0000 1.0000 0 0 0 1.0000 0.5000 1.0000 0 0 1.0000 0.7500 0.7500 1.0000 0 1.0000 0.2500 0.7500 -1.0000 1.0000U = 1.0000 1.0000 1.0000 1.0000 1.0000 0 4.0000 14.0000 34.0000 69.0000 0 0 -2.0000 -8.0000 -20.5000 0 0 0 -0.5000 -2.3750 0 0 0 0 -0.2500P = 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0Inv（A）求逆：inv(A)ans = 5.0000 -10.0000 10.0000 -5.0000 1.0000 -10.0000 30.0000 -35.0000 19.0000 -4.0000 10.0000 -35.0000 46.0000 -27.0000 6.0000 -5.0000 19.0000 -27.0000 17.0000 -4.00001.0000 -4.0000 6.0000 -4.0000 1.0000左除命令AEE=1 0 0 0 0;0 1 0 0 0;0 0 1 0 0;0 0 0 1 0;0 0 0 0 1;AEans = 5 -10 10 -5 1 -10 30 -35 19 -4 10 -35 46 -27 6 -5 19 -27 17 -4 1 -4 6 -4 1第2题程序：n=8;V=220;R=27; A=zeros(n,n);c=zeros(n,1); c(1)=V/R;A(1,1)=2;for i=1:n-1A(i,i+1)=-2;A(i+1,i)=-2/A(i,i);A(i+1,i+1)=5+2*A(i+1,i);end;for i=2:n c(i)=c(i)-A(i,i-1)*c(i-1);end;x(n)=c(n)/A(n,n);for k=n-1:-1:1 x(k)=(c(k)+2*x(k+1)/A(k,k);end;x运行结果：x =8.1478 4.0737 2.0365 1.0175 0.5073 0.2506 0.1194 0.0477第4题程序：（1）小题A=10 7 8 7;7 5 6 5;8 6 10 9;7 5 9 10;det(A),cond(A), eig(A)运行结果：ans = 1ans = 2.9841e+003ans = 0.0102 0.8431 3.8581 30.2887（2）小题A=10 7 8 7;7 5 6 5;8 6 10 9;7 5 9 10;b=32 23 33 31;deltaA=0 0.2 0.1 -0.1;0.08 0.07 0.02 0;0.2 -0.11 -0.04 0.01;-0.02 0.04 -0.03 -0.02;A1=A+deltaA;x=1 1 1 1;x1=A1b;deltax=x1-x;x1,deltaxx1 = 0.0077 2.3117 1.0211 1.0157deltax =-0.9923 1.3117 0.02110.0157norm(deltax),norm(x), B1= norm(deltax)/norm(x)ans =1.6449ans = 2B1 =0.8225norm(deltaA),norm(A),B2=norm(deltaA)/norm(A)ans = 0.2933ans = 30.2887B2 = 0.0097其中：deltax=，deltaA=，B1=，B2=。（3）小题A=10 7 8 7;7 5 6 5;8 6 10 9;7 5 9 10;b=32 23 33 31;D=rand(4);deltaA=0.5*10.(-4)*D;A1=A+deltaA;x=1 1 1 1;x1=A1b;deltax=x1-x;x1,deltaxans = 0.9991 1.0014 0.9997 1.0002ans = -0.0009 0.0014 -0.0003 0.0002norm(deltax),norm(x), B1= norm(deltax)/norm(x)ans = 0.0017ans = 2B1 = 8.2987e-004norm(deltaA),norm(A),B2=norm(deltaA)/norm(A)ans = 1.0824e-004ans = 30.2887B2 = 3.5738e-006其中：deltax= ，deltaA= ，B1= ，B2= 。第三章第1题（1）Jacobi迭代法A=10 1 2 3 4;1 9 -1 2 -3;2 -1 7 3 -5;3 2 3 12 -1;4 -3 -5 -1 15; b=12;-27;14;-17;12;x0=0 0 0 0 0;x=x0;error=0.001;N=1000;n=5;ax=0;for k=1:N for i=1:n ax=0; for j=1:n ax=ax+A(i,j)*x0(j); end ax=ax-A(i,i)*x0(i); x(i)=(b(i)-ax)/A(i,i); end if norm(x-x0)error break; else x0=x; endendxx =1.0019 -2.0017 2.9969 -1.9995 0.9978（2）G-S迭代法程序：A=10 1 2 3 4;1 9 -1 2 -3;2 -1 7 3 -5;3 2 3 12 -1;4 -3 -5 -1 15;b=12;-27;14;-17;12;x0=0 0 0 0 0;x=x0;error=0.001;N=1000;n=5;ax1=0;ax2=0;ax3=0;ax4=0;for k=1:N ax1=0; ax4=0; for j=2:n ax1=ax1+A(1,j)*x0(j); endx(1)=(b(1)-ax1)/A(1,1); for i=2:n-1 ax2=0;ax3=0; for j=1:i-1 ax2=ax2+A(i,j)*x(j); end for j=i+1:n ax3=ax3+A(i,j)*x0(j); end x(i)=(b(i)-ax2-ax3)/A(i,i); end for j=1:n-1 ax4=ax4+A(n,j)*x(j); end x(n)=(b(n)-ax4)/A(n,n); if norm(x-x0)=15*eps) m=m+1;h=h/2;n=2m,f2=f2+f3;s0=s; x=a+h:2*h:b-h;f3=sum(feval(fx,x); s=h/3*(f1+2*f2+4*f3);endI=s;（1）误差限为 ss=-5:0.001:5;fx=inline(cos(1/2.*x.*x),x);for i=1:1:10000I(i)=simpsonstep(fx,realmin,ss(i),1e-6);X(i)=I(i);endss=-5:0.001:5;fx=inline(sin(1/2.*x.*x),x);for i=1:1:10000I(i)=simpsonstep(fx,realmin,ss(i),1e-6);Y(i)=I(i);end （2）误差限为 程序：ss=-5:0.001:5;fx=inline(cos(1/2.*x.*x),x);for i=1:1:10000I(i)=simpsonstep(fx,realmin,ss(i),1e-10);X(i)=I(i);endss=-5:0.001:5;fx=inline(sin(1/2.*x.*x),x);for i=1:1:10000I(i)=simpsonstep(fx,realmin,ss(i),1e-10);Y(i)=I(i);end运行结果： 第八章第1题绘出函数y=f(x)的图形：x=-2:0.001:2;y=x.2+sin(10.*x)-1; s=0;plot(x,y)hold onplot(x,s)运行结果: 从图中观察，函数总共有十个零点。为保证牛顿法收敛到每一个解，需要将初值取得足够接近真解。取初值为x0=-1.5,编程：x0=-1.5;x1=x0;x2=x1-(x1.2+sin(10.*x1)-1)./(2.*x1+10.*cos(10.*x1);while abs(x2-x1)10-8 x1=x2;x2=x1-(x1.2+sin(10.*x