COLLOQUIUM
Spherical Splines on Clough-Tocher
Triangulations for Hermite
Interpolation
Department
of
Mathematics
Victoria Baramidze
Thursday,
October 15, 2009
4:00 p.m.
204 Morgan Hall
Abstract
Refreshments will be
served at 3:45 p.m.
Department of Mathematics
Western Illinois University
We construct spherical splines interpolating function
and its first order derivatives using minimal energy
approach. This approach has been used for arbitrary
planar triangulations. The lowest degree that can be
used in this case is five. Clough-Tocher macroelements allow us to use splines of degree 3. The use
of the macro-element allows us to reduce the size of
the linear system involved in the algorithm. A
spherical Hermite quasi-interpolant is studied first.
The optimal approximation result for the quasiinterpolant is used to obtain a bound for the error in
the prove that splines are minimizing energy
functionals with different homogeneous extensions
are equivalent: they all converge to the sampled
function, and the order of convergence is
independent of the extension.
We conclude with numerical examples that support
theoretical predictions.