Lifting MGARD: construction of (pre)wavelets on the interval using polynomial predictors of arbitrary order
<|reference_start|>Lifting MGARD: construction of (pre)wavelets on the interval using polynomial predictors of arbitrary order: MGARD (MultiGrid Adaptive Reduction of Data) is an algorithm for compressing and refactoring scientific data, based on the theory of multigrid methods. The core algorithm is built around stable multilevel decompositions of conforming piecewise linear $C^0$ finite element spaces, enabling accurate error control in various norms and derived quantities of interest. In this work, we extend this construction to arbitrary order Lagrange finite elements $\mathbb{Q}_p$, $p \geq 0$, and propose a reformulation of the algorithm as a lifting scheme with polynomial predictors of arbitrary order. Additionally, a new formulation using a compactly supported wavelet basis is discussed, and an explicit construction of the proposed wavelet transform for uniform dyadic grids is described.<|reference_end|>
@article{reshniak2024lifting,
    title={Lifting MGARD: construction of (pre)wavelets on the interval using
  polynomial predictors of arbitrary order},
    author={Viktor Reshniak, Evan Ferguson, Qian Gong, Nicolas Vidal, Rick
  Archibald, Scott Klasky},
    journal={arXiv preprint arXiv:2408.07212},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.07212},
    primaryClass={math.NA cs.NA math.FA}
}