e04fdf

e04fdf © Numerical Algorithms Group, 2002.

Purpose

E04FDF Unconstrained minimum of a sum of squares, combined Gauss-Newton and modified Newton algorithm using function values only (easy-to-use)

Synopsis

[x,fsumsq,w,ifail] = e04fdf(m,x<,ifail>)

Description

 
 This routine is applicable to problems of the form
 
                                   m         
                                   --        2
                    Minimize F(x)= >  [f (x)] 
                                   --   i    
                                   i=1       
 
                       T                                         
 where x=(x ,x ,...,x )  and m>=n. (The functions f (x) are often 
           1  2      n                             i             
 referred to as 'residuals'.) The user must supply a subroutine 
 LSFUN1 to evaluate functions f (x) at any point x.
                               i                  
 
 From a starting point supplied by the user, a sequence of points 
 is generated which is intended to converge to a local minimum of 
 the sum of squares. These points are generated using estimates of
 the curvature of F(x).

Parameters

e04fdf

Required Input Arguments:

m                                     integer
x (:)                                 real

Optional Input Arguments:                       <Default>

ifail                                 integer  -1

Output Arguments:

x (:)                                 real
fsumsq                                real
w (:)                                 real
ifail                                 integer

Fixed Name User-supplied Function

lsfun1                                function (User-Supplied)