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[Help-gsl] Solving a underdetermined nonlinear system

From: axplusbu
Subject: [Help-gsl] Solving a underdetermined nonlinear system
Date: Wed, 16 Mar 2016 20:37:39 -0400


I have a problem with p = 4 unknowns and n = 3 equations

i.e. p > n and my system is of the form:
f1(x1,x2,x3,x4) = 0
f2(x1,x2,x3,x4) = 0
f3(x1,x2,x3,x4) = 0

The multidimensional root finder "gsl_multiroots" requires p = n. The
nonlinear least-squares solver "gsl_multifit_nlin" requires n > p. (Note
this requirement appears to be absent from the documentation, the error
appears during compiling: "fsfsolver.c:37: ERROR: insufficient data points,
n < p.")

I could potentially transform my problem into a scalar minimization problem
and use "gsl_multimin". However, I currently have the Jacobian for the
above system and this would require me to re-derive the gradient for a new
scalar function which I would like to avoid.

Note: I was able to solve this problem in the past using the
Levenberg-Marquardt algorithm implemented in MATLAB's "fsolve".

Does there exist a solver in GSL that can solve my problem in its current
form? Or is anyone aware of another software package for doing so?


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