Frauke Sprengel
Periodic Interpolation and Wavelets on Sparse Grids
The paper is published: Numer. Algorithms, 17 (1-2) (1998), 147-169
65T10 Trigonometric approximation and interpolation
42B99 None of the above but in this section
Abstract: Nested Spaces of multivariate periodic functions forming a
non-stationary multiresolution analysis are investigated. The
scaling functions of these spaces are fundamental polynomials
of Lagrange interpolation on a sparse grid. The approach based
on Boolean sums leads to sample and wavelet spaces of significantly
lower dimension and good approximation order. The algorithms for
complete decomposition and reconstruction are of simple structure and
low complexity.

Keywords: Wavelets, Multivariate periodic interpolation, Boolean Sums, Sparse Grids