Posted by Michele Milano on September 24, 1998 at 21:39:00:

Hello,

I'm experiencing some convergence problems with lmder:

I would like to know, if someone had this problem before,

how to correctly tune the parameters, or a

suggestion on how to handle the problem in some other

way, if i'm misusing this subroutine somehow. the

problem is the following:

I have to do a least squares fitting to this model

(vectors are uppercase, scalars lowercase):

Y(i) = { yj[P,X(i)] }

where:

Y is the model output (a vector with n components)

yj[.] is the jth component of Y

j=1,...,n ranges on the n components of Y

i=1,...,m ranges on the m input/output pairs

P is the parameter vector

X is the model input

I use lmder in the following way:

I write the objective function to minimize as:

SUM(i=1,m SUM(j=1,n (dj(i) - yj[P,X(i)])^2 ) )

where dj(i) is the jth component of the ith observed

output vector D(i).

So, the total number of nonlinear functions to consider

is n*m, and the rows of the jacobian matrix are m*n as

well.

Now, my problem is that for one output component the

subroutine works fine, i.e. it always succeeds in

finding a reasonable minimum; when I increase the

number of outputs it stops very early, giving as information

that the tolerance on the parameters is too small.

If I start from this point and I continue the minimization

using the (in)famous numerical Recipes Levenberg-Marquardt

routine on the same function, it converges smoothly to

a reasonable point.

Now, since with one output I verified that the

performances of lmder are much better (a factor 10 or

so) w.r.t. the NR routine, what am I doing wrong here?

If there was some error in the computation of the

Jacobian, then I expected the NR routine to fail as

well, and anyway I checked the Jacobian routine

carefully, so I exclude such an eventuality...

Thanks in advance for any help,

Michele

- Re: nonlinear least squares of a multivariate function
**Michele Milano***20:53:54 9/25/98*(0)