Conjugate gradient heatbath for ill-conditioned actions

TL;DR

This paper introduces a conjugate gradient heatbath method for efficient sampling from ill-conditioned quadratic actions, outperforming local updates and offering greater stability and flexibility than global heatbath approaches.

Contribution

It proposes a novel conjugate gradient-based heatbath sampling technique that improves efficiency and stability for ill-conditioned quadratic actions.

Findings

Outperforms local updates for high condition number matrices

More stable than global heatbath methods

Allows for case-specific optimizations

Abstract

We present a method for performing sampling from a Boltzmann distribution of an ill-conditioned quadratic action. This method is based on heatbath thermalization along a set of conjugate directions, generated via a conjugate-gradient procedure. The resulting scheme outperforms local updates for matrices with very high condition number, since it avoids the slowing down of modes with lower eigenvalue, and has some advantages over the global heatbath approach, compared to which it is more stable and allows for more freedom in devising case-specific optimizations.