On Quasi-interpolation with non-uniformly distributed centers on Domains and Manifolds
- Maz´ya, Vladimir
- Schmidt, Gunther
2010 Mathematics Subject Classification
- 41A30 41A63 41A25
- Approximate approximations, multivariate quasi-interpolation, nonregular centers, manifolds
The paper studies quasi-interpolation by scaled shifts of a smooth and rapidly decaying function. The centers are images of a smooth mapping of the hZn-lattice in Rs, s ≥ n, and the scaling parameters are proportional to h. We show that for a large class of generating functions the quasi-interpolants provide high order approximations up to some prescribed accuracy. Although the approximants do not converge as h tends to zero, this is not feasible in computations if a scalar parameter is suitably chosen. The lack of convergence is compensated for by more flexibility in the choice of generating functions used in numerical methods for solving operator equations.
- J. Approx. Th. 10 (2001), pp. 125-145