数值解析matlab编程之非线性方程求根.docxVIP

1.二分法 function [ x,k ] = bisect( a,b,f,emg ) digits(8); if nargin 4 emg=1e-5; end max1=round((log(b-a)-log(emg))/log(2)); N=zeros(max1,2); k=0; while abs(b-a)emg fa=feval(f,a); fab=feval(f,(a+b)/2); if fab==0 x=(a+b)/2; return; elseif fa*fab0 b=(a+b)/2; else a=(a+b)/2; end N(k+1,1)=a; N(k+1,2)=b; k=k+1; end x=vpa((a+b)/2); vpa(N) 2.牛顿法 function [ x ] = Newton( fun2,x0,err ) digits(10); [f0,df]=feval(fun2,x0); if nargin3; err=1e-6; end if df==0; error(df=0 无解); end d=f0/df; i=1; while abs(d)err; x1=x0-d; [f0,df]=feval(fun2,x1); if df==0; error(df=0 无解); end x0=x1; d=f0/df; fprintf(x(%d)=%.10f err(%d)=%.10f\n,i,x1,i,d); i=i+1; end x=x1; 3.不动点迭代 function [ p0,i,err,p] = NMPiteration( f,p0,tol,max1 ) P(1)=p0; for i=1:max1 P(i+1)=feval(f,P(i)); %format compact err=abs(P(i+1)-P(i)); fprintf(err(%d)=%f\n,i,err); p=P(i); if(errtol) break; end if i==max1 disp(‘达到最大迭代次数，退出迭代); end end x=P 4.Steffensen迭代 function [ p0,i,err,p] = Steffensen( f,p0,tol,max1 ) P(1)=p0; for i=1:max1 y=feval(f,P(i)); z=feval(f,y); P(i+1)=P(i)-(y-P(i)).^2/(z-2*y+P(i)); %format compact err=abs(P(i+1)-P(i)); fprintf(err(%d)=%f\n,i,err); p=P(i); if(errtol) break; end if i==max1 disp(达到最大迭代次数，退出迭代); end end x=P