Modelling the discretization error of initial value problems using the Wishart distribution
Methodology
2023-08-15 v2 Numerical Analysis
Numerical Analysis
Optimization and Control
Statistics Theory
Data Analysis, Statistics and Probability
Statistics Theory
Abstract
This paper presents a new discretization error quantification method for the numerical integration of ordinary differential equations. The error is modelled by using the Wishart distribution, which enables us to capture the correlation between variables. Error quantification is achieved by solving an optimization problem under the order constraints for the covariance matrices. An algorithm for the optimization problem is also established in a slightly broader context.
Cite
@article{arxiv.2306.04084,
title = {Modelling the discretization error of initial value problems using the Wishart distribution},
author = {Naoki Marumo and Takeru Matsuda and Yuto Miyatake},
journal= {arXiv preprint arXiv:2306.04084},
year = {2023}
}