Low-Memory Numerical Certification

TL;DR

This paper presents a low-memory framework for certifying solutions to polynomial systems, utilizing solution iterators and spatial partitioning trees to reduce memory usage, with analysis and demonstration on large examples.

Contribution

It introduces a novel low-memory certification method for polynomial solutions, combining solution iterators and spatial partitioning trees.

Findings

Memory requirements are significantly reduced on large examples.

The proposed algorithm is analyzed for complexity.

Demonstrations confirm practical memory savings.

Abstract

We introduce a low-memory framework for certifying numerical solutions to polynomial systems which uses solution iterators and spatial partitioning trees to reduce memory requirements. We provide a prototypical algorithm, analyze its complexity, and demonstrate the memory reduction on a large example.