不动点迭代法的matlab实现

不动点迭代法（Fixed point iteration method）

原理网上已经很多了，这里不再赘述。
需要注意的是不动点迭代法的使用条件。

举个简单的例子，利用不动点法求解方程f(x) = 1 + 0.5*sin(x) − x = 0在（1,2）区间的根。
令g(x)=1+0.5*sin(x)

g = @(x) fun2(x);
% Initialization
x0 = 0;
tol = 1e-5;
maxIter = 40;

% Test biSection function
[xStar,xRoot] = fixPoint(g,x0,tol,maxIter);
fprintf('The fixed point is: %d\n',xStar);
fprintf('The root of the equation is: %d\n',xRoot);

function [xStar,xRoot] = fixPoint(fun2,x0,tol,maxIter)
% Inputs:
% fun2: a function handle, standing for the function written above
% x0: the initial guess of the fixed point
% tol: the tolerance within which the program can stop
% maxIter: the maximum number of iterations the program is allowed to run
% Outputs:
% xStar: the numerical value of the fixed point
% xRoot: the numerical value of the root

    x = zeros(maxIter,1);
    x(1) = fun2(x0);
    i = 1;

    while abs(fun2(x(i))-x(i))>tol && i