Surface Spline Approximation on SO(3). (arXiv:0911.1836v2 [math.CA] CROSS LISTED)

Surface Spline Approximation on SO(3). (arXiv:0911.1836v2 [math.CA] CROSS LISTED): "

The purpose of this article is to introduce a new class of kernels on SO(3)
for approximation and interpolation, and to estimate the approximation power of
the associated spaces. The kernels we consider arise as linear combinations of
Green's functions of certain differential operators on the rotation group. They
are conditionally positive definite and have a simple closed-form expression,
lending themselves to direct implementation via, e.g., interpolation, or
least-squares approximation. To gauge the approximation power of the underlying
spaces, we introduce an approximation scheme providing precise L_p error
estimates for linear schemes, namely with L_p approximation order conforming to
the L_p smoothness of the target function.

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