[Dune] [#571] MonomLocalInterpolation.interpolate() is extremly unstable

[Dune]

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User who did this - Carsten Gräser (Carsten) 

Attached to Project - Dune
Summary - MonomLocalInterpolation.interpolate() is extremly unstable
Task Type - Bug Report
Category - Localfunctions
Status - New
Assigned To - 
Operating System - Unspecified / All
Severity - Low
Priority - Normal
Reported Version - SVN
Due in Version - Undecided
Due Date - Undecided
Details - The method used to compute the weights in interpolate() is extremly unstable (and slow).

Even for 1d polynomials of order 9 the error in terms of the max norm of the coefficient vector goes up to ~0.6 if the coefficients range between -100 and 100. For order 11 the matrix seems even to be (numerically) singular. See results of testfem.cc. You may also try higher order polynomials and compare the speed with Pk3D.

Perhaps it's more stable (and efficient) to compute the monomial coefficients from the Newton- or Lagrange-interpolation.

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http://www.dune-project.org/flyspray/index.php?do=details&task_id=571

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