[Dune] [#571] MonomLocalInterpolation.interpolate() is extremly unstable
Dune
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Mon Jun 29 11:14:45 CEST 2009
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FS#571 - MonomLocalInterpolation.interpolate() is extremly unstable
User who did this - Carsten Gräser (Carsten)
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Obviously this is true. However the implementation pretends to be for arbitrary order but interpolate() is useless even for moderate order. This should at least be documented. But even for small orders the implemented algorithm seems to more unstable bad.
Using the straight forward implementation with Vandermonde matrix in 1d with matlab I get an error of about 1e-11 for order 5 and 5e-8 for order 10. The result is roughly the same for solving the linear systems and multiplying with the precomputed inverse. In contrast the current implementation gives and error of about 5e-8 for order 5 and 5e+1 for order 10. In my oppinion this is a really big difference.
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