Stability results for scattered‐data interpolation on Euclidean spheres Academic Article uri icon

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=1Majφ(dm(x,xj)), x ∈ Sm, where (aj)1M are real constants, φ : [0, π] → R is a fixed function, and (xj)1M is a set of distinct points in Sm. It is known that if φ is a strictly positive definite function in Sm, then the interpolation matrix (φ(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 φ, and provides stability estimates for the associated interpolation matrices. © J.C. Baltzer AG, Science Publishers.

author list (cited authors)

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

citation count

  • 14

publication date

  • April 1998