#571 MonomLocalInterpolation.interpolate() is extremly unstable
Metadata
| Property | Value |
|---|---|
| Reported by | Carsten Gräser (graeser@math.fu-berlin.de) |
| Reported at | Jun 28, 2009 14:40 |
| Type | Bug Report |
| Version | Git (pre2.4) [autotools] |
| Operating System | Unspecified / All |
| Last edited by | Carsten Gräser (graeser@math.fu-berlin.de) |
| Last edited at | Mar 4, 2013 23:11 |
| Closed by | Carsten Gräser (graeser@math.fu-berlin.de) |
| Closed at | Mar 4, 2013 23:11 |
| Closed in version | Unknown |
| Resolution | Won't fix |
| Comment | The instability is documented now. |
| More stable implementations are welcome. |
Description
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.