Construction of Laguerre pseudospectral differentiation matrices
Numerical Analysis
2026-04-23 v1 Numerical Analysis
Abstract
In this paper, we present a stable and efficient approach for constructing Laguerre pseudospectral differentiation matrices. The proposed method reformulates the off-diagonal entries and computes all required quantities simultaneously using an existing fast algorithm that also generates the collocation nodes. For the diagonal entries, a closed-form expression is employed to improve numerical accuracy. This construction avoids the catastrophic cancellation present in classical formulations and yields an all-in-one procedure for generating differentiation matrices. Numerical experiments demonstrate improved robustness and sustained high accuracy for significantly larger numbers of collocation points compared to standard implementations.
Cite
@article{arxiv.2604.20536,
title = {Construction of Laguerre pseudospectral differentiation matrices},
author = {Emma Nel and Nicholas Hale},
journal= {arXiv preprint arXiv:2604.20536},
year = {2026}
}