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Erschienen in:
2006 | OriginalPaper | Buchkapitel
A Convergence Problem in Collocation Theory
Erschienen in: Mathematical Foundation of Geodesy
Verlag: Springer Berlin Heidelberg
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Collocation theory allows the approximation of the anomalous potential
T
, harmonic in a region
Ω
, by a smoother function
$$ \hat T $$
harmonic in a larger domain
Σ
and agreeing with measurements performed on
T
at discrete points. The smoothing least-squares collocation method is a part of collocation theory in which a hybrid norm is minimized, norm that depends upon a parameter
λ
that can be interpreted as the relative weight of the norm of
$$ \hat T $$
in
Σ
and in
Ω
.
The problem of the behaviour of
$$ \hat T $$
when the number of measurements tends to infinity and contemporarily
λ
→ ∞ is analyzed: the convergence to the correct solution is proved under suitable hypotheses.