e04gcf

e04gcf © Numerical Algorithms Group, 2002.

Purpose

E04GCF Unconstrained minimum of a sum of squares, combined Gauss-Newton and quasi-Newton algorithm, using 1st derivatives (easy-to-use)

Synopsis

[x,fsumsq,w,ifail] = e04gcf(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 
 LSFUN2 to evaluate the residuals and their first derivatives at 
 any point x.
 
 Before attempting to minimize the sum of squares, the algorithm 
 checks LSFUN2 for consistency. Then, 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

e04gcf

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

lsfun2                                function (User-Supplied)