Periodic interpolation and wavelets on sparse grids
The author investigates nested spaces of multivariate periodic functions forming a non-stationary multiresolution analysis. The scaling functions of these spaces are 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 presented have a simple structure and a low complexity of \(O(j^22^j)\) essential operations for the level \(j\).
scientific article; zbMATH DE number 1185568