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Approximation Order
Approximation Scheme
Differential Operators
Error Estimate
Least Squares Approximation
Numerical Analysis
Positive Definite
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Surface Spline Approximation on SO(3)
Surface Spline Approximation on SO(3),Thomas Hangelbroek,Dominik Schmid
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Surface Spline Approximation on SO(3)
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Citations: 2
)
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Thomas Hangelbroek
,
Dominik Schmid
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 closedform expression, lending themselves to direct implementation via, e.g., interpolation, or leastsquares 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.
Published in 2009.
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References
(17)
Radial Basis Functions : Theory and Implementations
(
Citations: 278
)
M. D. Buhmann
Published in 2003.
On the fast rotation function
(
Citations: 12
)
J. Navaza
Journal:
Acta Crystallographica Section A  ACTA CRYSTALLOGR A
, vol. 43, no. 5, pp. 645653, 1987
Approximation using scattered shifts of a multivariate function
(
Citations: 7
)
Ronald DeVore
,
Amos Ron
Journal:
Transactions of The American Mathematical Society  TRANS AMER MATH SOC
, vol. 362, no. 12, pp. 62056205, 2010
Stability results for approximation by positive definite functions on SO(3)
(
Citations: 9
)
Frank Filbir
,
Dominik Schmid
Journal:
Journal of Approximation Theory  JAT
, vol. 153, no. 2, pp. 170183, 2008
Representations of the Rotation and Lorentz Groups and Their Applications
(
Citations: 103
)
I. M. Gel'fand
,
R. A. Minlos
,
Z. Ya. Shapiro
,
G. Cummins
,
T. Boddington
,
H. K. Farahat
,
J. E. Mansfield
Journal:
Physics Today  PHYS TODAY
, vol. 17, no. 8, 1964
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Citations
(2)
Kernel Approximation on Manifolds II: The $L_{\infty}$norm of the $L_2$projector
Thomas Hangelbroek
,
Fran J Narcowich
,
Xingping Sun
,
Joe D Ward
Published in 2010.
Polyharmonic and Related Kernels on Manifolds: Interpolation and Approximation
Thomas Hangelbroek
,
Fran J. Narcowich
,
Joe D. Ward
Published in 2010.