falsepos.m

matlab算法集 matlab算法集

function [x,k] = falsepos (x0,x1,tol,m,f)
%----------------------------------------------------------------
% Usage:       [x,k] = falsepos (x0,x1,tol,m,f)
%
% Description: Apply the false position method to find a root of:
%
%                   f(x) = 0
%
% Inputs:       x0  = lower limit of search
%               x1  = upper limit of search (x1 > x0)
%               tol = error tolerance used to terminate search 
%                     (tol >= 0)
%               m   = maximum number of iterations (m >= 1)
%               f   = string containing name of user-supplied
%                     function.  The function f is of the form:
%
%                     function y = f(x)
%
% Outputs:      x = Estimated root of f(x) = 0 
%               k = number of iterations performed. If k < m,
%                   then the following convergence criterion
%                   was satisfied:
%
%                   |f(x)| < tol
%   
% Notes:        1. x0 and x1 must be selected such that 
%                  f(x0)*f(x1) < 0 to ensure that there is a 
%                  root in [x0,x1]
%----------------------------------------------------------------

% Initialize 
   
   k = 0;
   x1  = args (x1,x0,x1,2,'falsepos');
   tol = args (tol,0,tol,3,'falsepos');
   m   = args (m,1,m,4,'falsepos');
   f0 = feval(f,x0); 
   f1 = feval(f,x1);
   if f0*f1 >= 0
      fprintf ('\nIn falsepos, x0 and x1 must bracket a root.\n');
      return
   end

% Find root 
     
   y = tol + 1;   
   while (y > tol) & (k <= m)
      x2 = x1 - (x1-x0)*f1/(f1-f0);
      f2 = feval(f,x2);
      if f0*f2 < 0
         x1 = x2;
         f1 = f2; 
      else 
         x0 = x2;
         f0 = f2; 
      end
      y = abs(f2);
      k = k + 1;
   end
   x = x2;