🚀 go-pugleaf

In article <1992Sep3.064230.42744@kuhub.cc.ukans.edu> jeff@kuhub.cc.ukans.edu (Jeff Bangert) writes:
>A chemist has asked me to solve a problem: she has data and a model
>which is to be fit by 'least squares'.  It looks like non-linear
>regression, except that:
>
>    1. the model has two equations
>    2. both are non-linear
>    3. there are parameters common to the two equations.
>
>I would like to know:
>
>    1. is there a 'standard' method for solving this problem?
>    2. is there literature in stat or chemistry which I could read?
>

  The problem is to minimize the properly weighted sum of squares of the
  corrections ( residuals) of the *observations* (not the defects of the
  equations!) subject to the constraints given by the model equation
  system.   This leads to a constrained leaast-squares minimization.

  The minimization (least squares with model equations in form of simultaneous
  nonlinear equations) is discussed and an algorithm for the solution
  proposed in
 

   A. Celmins, Least-Squares Optimization with Implicit Model Functions, in
   "Mathematical Programming with Data Perturbations II", Anthony V. Fiacco,
   Ed., Marcel Dekker, 1983, pp. 131-152.

 
  Aivars Celmins
  celms@brl.mil
  (410)-278-6986