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Article #172

Nonlinear Least Squares

#172
From: Chris Paredis
Date: Sun, 02 Aug 1992 22:27
28 lines
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I'm looking for an algorithm that can solve underdetermined nonlinear least
square problems:

           T
     Min (R .R)     where R    is a nonlinear vector function of X
                           mx1                                    nx1

     and m<n.


The Gauss-Newton algorithm converges quadratically for zero residual
problems (ZRP) but converges very slowly for large residual problems.
The LRP can be solved faster using BFGS for instance.
Now, I need a routine that can solve both ZRP and LRP with at least
superlinear convergence.
Fletcher and Xu, have proposed a hybrid algorithm (combination of GN and
BFGS) for overdetermined problems (m>n), but this cannot by easily adapted
for underdetermined problems (the Hessian appoximation J'*J will always be
singular)

Any hints ??

  ** Chris **

Chris J.J. Paredis				Email: Paredis@cmu.edu
Electrical and Computer Engineering		phone: (412)-268-7121
The Robotics Institute				Carnegie - Mellon University
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From: cjp+@IUS4.IUS.CS.CMU.EDU (Chris Paredis)
Newsgroups: sci.math.num-analysis
Subject: Nonlinear Least Squares
Message-ID: <1992Aug02.222719.253771@cs.cmu.edu>
Date: 2 Aug 92 22:27:19 GMT
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