二分法,不动点迭代法,艾特肯加速迭代法,牛顿切线法的matlab程序及举例.docVIP

§2.1.1 二分法的MATLAB主程序 function [k,x,wuca,yx]=erfen(a,b,abtol) a(1)=a; b(1)=b; ya=fun(a(1)); yb=fun(b(1)); %程序中调用的fun.m 为函数 if ya* yb0, disp(注意：ya*yb0,请重新调整区间端点a和b.), return end max1=-1+ceil((log(b-a)- log(abtol))/ log(2)); % ceil是向 方向取整 for k=1: max1+1 a;ya=fun(a); b;yb=fun(b); x=(a+b)/2; yx=fun(x); wuca=abs(b-a)/2; k=k-1; [k,a,b,x,wuca,ya,yb,yx] if yx==0 a=x; b=x; elseif yb*yx0 b=x;yb=yx; else a=x; ya=yx; end if b-a abtol , return, end end k=max1; x; wuca; yx=fun(x); §2.1.2 不动点迭代法的MATLAB主程序 function [k,piancha,xdpiancha,xk,yk]=diedai2(x0,tol,ddmax) x(1)=x0; for i=1: ddmax x(i+1)=fun(x(i));piancha=abs(x(i+1)-x(i)); xdpiancha=piancha/( abs(x(i+1))+eps);i=i+1; xk=x(i);yk=fun(x(i)); [(i-1) piancha xdpiancha xk yk] if (pianchatol)|(xdpiancha tol) k=i-1; xk=x(i); return; end end if iddmax disp(迭代次数超过给定的最大值ddmax) k=i-1; xk=x(i);yk=fun(x(i)); [(i-1) piancha xdpiancha xk yk]; return; end P=[(i-1),piancha,xdpiancha,xk,yk]; §2.1.3 艾特肯加速迭代法的MATLAB主程序 function [k,xk,yk,p]= Aitken (x0,tol, ddmax) x(1)=x0; for i=1: ddmax x1(i+1)=fun(x(i)); x2(i+1)=fun(x1(i+1)); x(i+1)=x2(i+1)-(x2(i+1)-x1(i+1))^2/(x2(i+1)-2*x1(i+1)+ x(i)); piancha=abs(x(i+1)-x(i)); xdpiancha= piancha/( abs(x(i+1))+eps); i=i+1; xk=x(i);yk=fun(x(i)); if (pianchatol)|(xdpianchatol) k=i-1; xk=x(i); yk=fun(x(i)); m=[0,1:i-1]; p=[m,x1,x2,x]; return; end end if iddmax disp(迭代次数超过给定的最大值ddmax) k=i-1; xk=x(i); yk=fun(x(i)); m=[0,1:i-1]; p=[m,x1,x2,x]; return; end m=[0,1:i-1]; p=[m,x1,x2,x]; §2.1.4 牛顿切线法的MATLAB主程序 function [k,xk,yk,piancha,xdpiancha]=newtonqx(x0,tol,ftol,gxmax) x(1)=x0; for i=1: gxmax x(i+1)=x(i)-fun(x(i))/(dfun(x(i))+eps); piancha=abs(x(i+1)-x(i)); xdpiancha= piancha/( abs(x(i+1))+eps); i=i+1; xk=x(i);yk=fun(x(i)); [(i-1) xk yk piancha xdpiancha] if (abs(yk)ftol)((pianchatol)|(xdpiancha tol)) k=i-1; xk=x(i);[(i-1) xk yk piancha xdpiancha] return; end end if igxmax disp(请注意：迭代次数超过给定的最大值gxma