Reconstruction Plans and Efficient Rank-1 Lattice Construction for Chebyshev Expansions Over Lower Sets

TL;DR

This paper develops efficient methods for constructing rank-1 lattices to accurately reconstruct Chebyshev expansion functions over lower sets, improving computational efficiency and memory usage.

Contribution

It introduces a heuristic CBC algorithm for optimal lattice construction and establishes equivalence of reconstruction plans under certain conditions.

Findings

Efficient rank-1 lattices enable exact Chebyshev function reconstruction.

The heuristic CBC algorithm improves computational and memory efficiency.

Reconstruction plans are shown to be equivalent under specific lower set conditions.

Abstract

This study focuses on constructing efficient rank-1 lattices that enable the exact integration and reconstruction of functions within Chebyshev spaces, based on finite lower index sets. We establish the equivalence of different reconstruction plans under specific conditions for certain lower sets. Furthermore, we introduce a heuristic component-by-component (CBC) algorithm that efficiently identifies admissible generating vectors and suitable numbers of nodes $n$, optimizing both memory usage and computational time.