regula.m

国外计算机科学教材系列 numerial method using matlab (third edition)

function [c,err,yc]=regula(f,a,b,delta,epsilon,max1)

%Input - f is the function input as a string 'f'
%	    - a and b are the left and right endpoints
%	    - delta is the tolerance for the zero
%	    - epsilon is the tolerance for the value of f at the zero
%	    - max1 is the maximum number of iterations
%Output - c is the zero
%	     - yc=f(c)
%	     - err is the error estimate for c

% NUMERICAL METHODS: MATLAB Programs
%(c) 1999 by John H. Mathews and Kurtis D. Fink
%To accompany the textbook:
%NUMERICAL METHODS Using MATLAB,
%by John H. Mathews and Kurtis D. Fink
%ISBN 0-13-270042-5, (c) 1999
%PRENTICE HALL, INC.
%Upper Saddle River, NJ 07458

ya=feval(f,a);
yb=feval(f,b);

if ya*yb>0
	disp('Note: f(a)*f(b) >0'),
	break,
end

for k=1:max1
	dx=yb*(b-a)/(yb-ya);
	c=b-dx;
	ac=c-a;
	yc=feval(f,c);
	if yc==0,break;
	elseif yb*yc>0
		b=c;
		yb=yc;
	else
		a=c;
		ya=yc;
	end
	dx=min(abs(dx),ac);
	if abs(dx)<delta,break,end
	if abs(yc)<epsilon, break,end
end

c;
err=abs(b-a)/2;
yc=feval(f,c);