1 function g=dichotomy(f,tol) 2 %this routine uses bisection to find a zero of user-supplied 3 %continuous function f.the user must supply two points an and bn 4 %such that f(an) and f(bn) have different signs .the user also 5 %supplies a convergence tolerance delta . 6 %this progress is writen by H.D.dong 7 % tic; 8 % clear 9 % clc 10 % f=inline('x^3-x^2-1'); 11 % f=inline('x^6-x-1'); 12 % f=inline('x^2+1'); 13 % % h=inline('x^3-x^2-1'); 14 % % tol=1e-14; 15 % % Provides a zero-point presence interval 16 % % % 17 % % an=1; 18 % % bn=2; 19 % % % 20 % % root=dichotomy(h,tol) 21 an=1; 22 bn=2; 23 root=0; 24 if f(an)==0,root=an;bn=root;return; 25 elseif f(bn)==0,root=bn;an=root;return; 26 elseif sign(f(an))==sign(f(bn)),fprintf('There is no solution in this equation!'); 27 %% 28 %Above showed:there have considered that we have found the root in the first step. 29 else 30 k=0; 31 while (bn-an)>=tol 32 midpoint=(bn+an)/2;k=k+1;F(k)=f(midpoint); 33 if f(midpoint)==0,root=midpoint;an=root;bn=root;break; 34 elseif sign(f(midpoint))~=sign(f(an)),bn=midpoint; 35 else 36 an=midpoint; 37 end 38 end 39 root=(bn+an)/2; 40 end 41 g=root; 42 % toc;