Least-squares applications often present themselves as fitting goals such as
(60)
(61)
To balance our possibly contradictory goals we need weighting functions.
The quadratic form that we should minimize is
(62)
where
is the inverse multivariate spectrum of the noise
(data-space residuals) and
is the inverse multivariate spectrum of the model.
In other words,
is a leveler on the data fitting error and
is a leveler on the model.
There is a curious unresolved issue:
What is the most suitable constant scaling ratio
of
to
?