Error estimates for scattered data interpolation on spheres Academic Article

abstract

• We study Sobolev type estimates for the approximation order resulting from using strictly positive definite kernels to do interpolation on the n-sphere. The interpolation knots are scattered. Our approach partly follows the general theory of Golomb and Weinberger and related estimates. These error estimates are then based on series expansions of smooth functions in terms of spherical harmonics. The Markov inequality for spherical harmonics is essential to our analysis and is used in order to find lower bounds for certain sampling operators on spaces of spherical harmonics.

authors

• Ward, Joseph

published proceedings

• MATHEMATICS OF COMPUTATION

author list (cited authors)

• Jetter, K., Stockler, J., & Ward, J. D.

citation count

• 98

complete list of authors

• Jetter, K||Stockler, J||Ward, JD

publication date

• April 1999

publisher

• American Mathematical Society (AMS)  Publisher

published in

• Mathematics of Computation  Journal

keywords

• Best Approximation
• Markov Inequality
• Norming Set
• Scattered Data Interpolation
• Spherical Harmonics

Digital Object Identifier (DOI)

• 10.1090/S0025-5718-99-01080-7

start page

• 733

end page

• 747

volume

• 68

issue

• 226

URL

• http%3A%2F%2Fdx.doi.org%2F10.1090%2Fs0025-5718-99-01080-7