c05nbf

c05nbf © Numerical Algorithms Group, 2002.

Purpose

C05NBF Solution of system of nonlinear equations using function values only (easy-to-use)

Synopsis

[x,fvec,ifail] = c05nbf(fcn,x<,xtol,ifail>)

Description

 
 The system of equations is defined as:
 
               f (x ,x ,...,x )=0, for i=1,2,...,n.
                i  1  2      n        
 
 C05NBF is based upon the MINPACK routine HYBRD1. It chooses the
 correction at each step as a convex combination of the Newton 
 and scaled gradient directions. Under reasonable conditions 
 this guarantees global convergence for starting points far from
 the solution and a fast rate of convergence. The Jacobian is 
 updated by the rank-1 method of Broyden. At the starting point 
 the Jacobian is approximated by forward differences, but these 
 are not used again until the rank-1 method fails to produce 
 satisfactory progress.

Parameters

c05nbf

Required Input Arguments:

fcn                                   function (User-Supplied)
x (:)                                 real

Optional Input Arguments:                       <Default>

xtol                                  real     sqrt(eps)
ifail                                 integer  -1

Output Arguments:

x (:)                                 real
fvec (:)                              real
ifail                                 integer