3 papers
math.NA2023
Sparse Spectral Methods for Solving High-Dimensional and Multiscale Elliptic PDEs
Craig Gross, Mark Iwen
In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claimed that, regarding Fourier spectral methods for solving differential equations, ``[t]he virtues of the Fast…
math.NA2020
Sparse Fourier Transforms on Rank-1 Lattices for the Rapid and Low-Memory Approximation of Functions of Many Variables
Craig Gross, Mark Iwen, Lutz Kämmerer +1
We consider fast, provably accurate algorithms for approximating functions on the -dimensional torus, , that are sparse (or compressibl…
math.NA2020
A Deterministic Algorithm for Constructing Multiple Rank-1 Lattices of Near-Optimal Size
Craig Gross, Mark A. Iwen, Lutz Kämmerer +1
In this paper we present the first known deterministic algorithm for the construction of multiple rank-1 lattices for the approximation of periodic functions of many variables. The…