Computational complexity of solving polynomial differential equations over unbounded domains with non-rational coefficients

TL;DR

This paper extends the complexity analysis of solving polynomial differential equations over unbounded domains to include non-rational coefficients, using Computable Analysis to handle arbitrary inputs and analyze the operator's complexity.

Contribution

It generalizes previous results to non-rational coefficients and provides a uniform complexity analysis of the solution operator within Computable Analysis.

Findings

Extended complexity results to non-rational coefficients

Provided a uniform complexity analysis of the solution operator

Utilized Computable Analysis framework for arbitrary inputs

Abstract

In this note, we extend the result of \cite{PoulyG16} about the complexity of solving polynomial differential equations over unbounded domains to work with non-rational input. In order to deal with arbitrary input, we phrase the result in framework of Conputable Analysis \cite{Ko91}. As a side result, we also get a uniform result about complexity of the operator, and not just about the solution.