二分法求方程的根(Matlab)

二分法在很多地方应该都会见到，这里是通过迭代逼近的方法求出一个方程的根。

function xc = bisection(f,a,b,tol)
% use the bisection method to find the root of the function
% Page 30,computer problem 7(Bisection method)
% input:
% f:the function that transform from the equation
% a,b:the left and right value of the interval which the root is in
% tol:the accuracy
% output:
% xc:the solution of the equation
if sign(f(a)) * sign(f(b)) >=0
    error('f(a)f(b)<0 not satisfied!')
end
if nargin < 3
    disp('The function should at least include 3 parameters');
end
if nargin == 3
    tol = 10^-6;
end
while (b-a)/2 > tol
    c = (a + b)/2;     
    if f(c) == 0         % when f(c) == 0,c is a root of the function
        break 
    end
    if f(a) * f(c) < 0    % a and c form a new interval
        b = c;
    else                  % c and b form a new interval
        a = c;
    end
end
xc = (a+b)/2;             % the mid_rang is the root that we find