Title: Reconstruction Plans and Efficient Rank-1 Lattice Construction for Chebyshev Expansions Over Lower Sets Show Chinese title

Title: 重构计划和用于下集上切比雪夫展开的高效秩-1格构构造

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. Show Chinese abstract

Abstract: 本研究专注于构建高效的秩-1格子，这些格子能够在切比雪夫空间内实现函数的精确积分和重构，基于有限的下标集合。 我们在特定条件下建立了某些下标集合下不同重构方案的等价性。 此外，我们引入了一种启发式的逐成分（CBC）算法，该算法能够高效地确定可接受的生成向量和合适的节点数$n$，优化内存使用和计算时间。