数值计算方法上机答案.doc

本科实验报告课程名称:实验项目:实验地点:机房专业班级:采矿1206学号:学生姓名:康明月指导教师:2014年7月3日求非线性方程的根。求方程在附近的是根,要求精度满足.(牛顿切线法)f=inline('x-cos(x)');%f(x)df=inline('1+sin(x)');%f'(x)n=1;x0=input('x0=');del=input('del=');N=input('N=');fprintf('\nkx(k)');fprintf('\n%2d%f',0,x0);F0=f(x0);dF0=df(x0);whilen<NifdF0==0fprintf('导数为0,迭代无法继续进行.');return;endx1=x0-F0/dF0;F1=f(x1);dF1=df(x1);if((abs(x1-x0)<del)|abs(F1)<del)fprintf('\n\n结果:%f\n',x1);return;endfprintf('\n%2d%f',n,x1);n=n+1;x0=x1;F0=F1;dF0=dF1;endfprintf('\n\n%d次迭代后未达到精度要求.\n',N);NewtonIterationx0==1e-4N=100kx(k):,求出具有思维有效数字的根近似值..(简单迭代法)clearclcphi=inline('(+x^2)^(1/3)');%迭代函数x0=input('x0=');del=input('del=');N=input('N=');n=1;fprintf('\n%2d%f',0,x0);whilen<Nx=phi(x0);ifabs(x-x0)<delfprintf('\n\n近似解=%f\n',x);returnendfprintf('\n%2d%f',n,x);n=n+1;x0=x;endfprintf('\n\n%fd次迭代后未达到精度要求.\n',N)x0=1del=1e-4N==(直接法或迭代法)1、(列主元素消元法)a=input('a=')%[2,2,1,-3,8;-2,1,-1,-3,1;8,-1,3,8,-1;10,4,4,3,8];[p,n]=size(a);forw=1:p[x,y]=find(a(w:p,w)==max(max(a(w:p,w))));q=a(w,:);a(w,:)=a(x,:);a(x,:)=q;endforj=1:(p-1)fori=(j+1):pa(i,:)=a(j,j)/a(i,j).*a(i,:)-a(j,:);endendm=p;whilem>1s(m)=a(m,n);j=p;while((j>2)&(j>=m+1)&(j<n))s(m)=s(m)-a(m,j)*x(j);j=j-1;endx(m)=s(m)/a(m,m);m=m-1;xenda=[221-38;-21-1-31;8-138-1;104438]a=221-38-21-1-318-138-1104438x=--[x,det,flag]=Gauss(A,b)[n,m]=size(A);nb=length(b);ifn~=merror('therowsandcloumsofAmustbeequal!');return;endifm~=nberror('therowsandcloumsofAmustbeequalthelengthofb!');return;endflag='OK';det=1;x=zeros(n,1);fork=1:(n-1)max1=0;fori=k:nifabs(A(i,k))>max1max1=abs(A(i,k));r=i;endendifmax1<1e-6flag='failure';return;endifr>kforj=k:nz=A(k,j);A(k,j)=A(r,j);A(r,j)=z;endz=b(k);b(k)=b(r);b(r)=z;det=-det;endfori=k+1:nm=A(i,k)/A(k,k);forj=k+1:nA(i,j)=A(i,j)-m*A(k,j);endb(i)=b(i)-m*b(k);enddet=det*A(k,k);enddet=det*A(n,n);ifabs(A(n,n))<1e-6flag='faliure';return;endfork=n:-1:1forj=k+1:nb(k)=b(k)-A(k,j)*x(j);endx(k)=b(k