Code covered by the BSD License

Numerical Methods Using MATLAB, 4e

John Mathews (view profile)

23 Dec 2003 (Updated )

Companion software to accompany the book "Numerical Methods Using MATLAB"

[p1,err,k,y]=secant(f,p0,p1,delta,epsilon,max1)
```function [p1,err,k,y]=secant(f,p0,p1,delta,epsilon,max1)

%Input    - f is the object function
%            - p0 and p1 are the initial approximations to a zero of f
%	         - delta is the tolerance for p1
%	         - epsilon is the tolerance for the function values y
%	         - max1 is the maximum number of iterations
%Output - p1 is the secant method approximation to the zero
%	         - err is the error estimate for p1
%	         - k is the number of iterations
%	         - y is the function value f(p1)

%If f is defined as an M-file function use the @ notation
% call [c,err,yc]=bisect(@f,a,b,delta).
%If f is defined as an anonymous function use the
% call [c,err,yc]=bisect(f,a,b,delta).

%  NUMERICAL METHODS: Matlab Programs
% (c) 2004 by John H. Mathews and Kurtis D. Fink
%  Complementary Software to accompany the textbook:
%  NUMERICAL METHODS: Using Matlab, Fourth Edition
%  ISBN: 0-13-065248-2
%  Prentice-Hall Pub. Inc.
%  One Lake Street
%  Upper Saddle River, NJ 07458

for k=1:max1
p2=p1-f(p1)*(p1-p0)/(f(p1)-f(p0));
err=abs(p2-p1);
relerr=2*err/(abs(p2)+delta);
p0=p1;
p1=p2;
y=f(p1);
if (err<delta)|(relerr<delta)|(abs(y)<epsilon),break,end
end

```