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 | Model fitting by least squares |  |
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Methods of physics may
relate modeled data
to model parameters
,
with a nonlinear relation,
say
.
The power-series approach then leads to
representing modeled data as:
 |
(107) |
where
is the matrix of partial derivatives
of data values by model parameters,
say
,
evaluated at
.
The modeled data
minus
the observed data
is the residual we minimize.
It is worth noticing that the residual updating
(109)
in a nonlinear application is the same
as that in a linear application (55).
If you make a large step
, however,
the new residual
is different from that expected by
(109).
Thus,
you should always re-evaluate the residual vector at the new location,
and if you are reasonably cautious,
you should be sure the residual norm has actually decreased
before you accept a large step.
The pathway of inversion with physical nonlinearity
is well developed in the academic literature,
and Bill Symes at Rice University has a particularly active group.
There are occasions to change the weighting function during model fitting.
Then,
one simply restarts the calculation from the current model.
In the code,
you would flag a restart with the expression forget=true.
 |
 |
 |
 | Model fitting by least squares |  |
![[pdf]](icons/pdf.png) |
Next: Coding nonlinear fitting problems
Up: THE WORLD OF CONJUGATE
Previous: THE WORLD OF CONJUGATE
2014-12-01