PreprintCC BY 4.0arXiv
The Effect of Quadrature on the Convergence of Policy Iteration for Hamilton-Jacobi-Bellman Equations
Abstract
Modern finite element libraries allow users to express partial differential equations directly in variational form, with the added convenience of automatic quadrature selection. In the context of Hamilton-Jacobi-Bellman (HJB) equations, automatic quadrature selection can result in nonmatching quadratures between different terms that may lead to loss of convergence of the policy iteration, which is otherwise expected from theory to converge superlinearly. The simple remedy of enforcing matching quadrature recovers the expected superlinear convergence.
Versions
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BibTeX
@misc{hall2026effect,
title = {{The Effect of Quadrature on the Convergence of Policy Iteration for Hamilton-Jacobi-Bellman Equations}},
author = {Thomas Hall and Iain Smears and Endre Süli and Harry Wells},
howpublished = {arXiv},
year = {2026},
month = jun,
doi = {10.48550/arxiv.2606.24806},
eprint = {2606.24806},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.24806},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Effect of Quadrature on the Convergence of Policy Iteration for Hamilton-Jacobi-Bellman Equations
AU - Thomas Hall
AU - Iain Smears
AU - Endre Süli
AU - Harry Wells
PY - 2026
DA - 2026/06/23
PB - arXiv
DO - 10.48550/arxiv.2606.24806
UR - https://arxiv.org/abs/2606.24806
AB - Modern finite element libraries allow users to express partial differential equations directly in variational form, with the added convenience of automatic quadrature selection. In the context of Hamilton-Jacobi-Bellman (HJB) equations, automatic quadrature selection can result in nonmatching quadratures between different terms that may lead to loss of convergence of the policy iteration, which is otherwise expected from theory to converge superlinearly. The simple remedy of enforcing matching quadrature recovers the expected superlinear convergence.
ER -