Permanence Property in Spherical Spline Interpolation.

摘要

Spherical spline functions are introduced by use of Green's (surface) functions with respect to the Beltrami operator on the sphere. The method of interpolation by spherical splines is formulated as variational problem of minimizing a (Sobolev) 'energy' norm under interpolatory constraints. The process is constructed so as to have the so - called performance property, i.e. the transition from the interpolating spline with respect to N data to the interpolating spline with respect to N + 1 data necessitates merely the addition of one more term, all the terms obtained formerly remaining unchanged. The algorithm is numerically stable and very economical as regards the number of operations.