Stability results for scattered-data interpolation on Euclidean spheres

abstract

• Let Sm denote the unit sphere in Rm+1 and dm the geodesic distance in Sm. A spherical-basis function approximant is a function of the form s(x) = j=1Maj(dm(x,xj)), x Sm, where (aj)1M are real constants, : [0, ] R is a fixed function, and (xj)1M is a set of distinct points in Sm. It is known that if is a strictly positive definite function in Sm, then the interpolation matrix ((dm(xj, xk)))j,k=1M is positive definite, hence invertible, for every choice of distinct points (xj)1M and every positive integer M. The paper studies a salient subclass of such functions , and provides stability estimates for the associated interpolation matrices. J.C. Baltzer AG, Science Publishers.

authors

• Narcowich, Francis
• Sivakumar, Natarajan
• Ward, Joseph

published proceedings

• ADVANCES IN COMPUTATIONAL MATHEMATICS

author list (cited authors)

• Narcowich, F. J., Sivakumar, N., & Ward, J. D.

citation count

• 14

complete list of authors

• Narcowich, FJ||Sivakumar, N||Ward, JD

publication date

• April 1998

publisher

• Springer Nature  Publisher

published in

• Advances in Computational Mathematics  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1023/A:1018996230401

start page

• 137

end page

• 163

volume

• 8

issue

• 3

URL

• http://dx.doi.org/10.1023/a:1018996230401