N-Dimensional Multiresolution Algorithms for Point Values

Abstract: Multiresolution algorithms are used in several applications in order to attain data compression, denoising or computional time reduction in algorithms dealing with large data. Our objective is to introduce nonlinear reconstructions in the N-dimensional case and compare their performances when applied with and without error control algorithms. This paper describes then the N-dimensional multiresolution algorithms with and without error control strategies in discrete point values as a generalization to N dimensions of the work done in this direction, see [13], [14], [11], [2], [16]. Some numerical experiments are included to exemplify the utility of these algorithms. In the results it can be observed that nonlinear stable methods improve their linear counterparts in presence of discontinuities in the data. Even non-stable nonlinear methods can overcome the instabilities and get better results than linear ones when used with error control.