Contributed Discussion of "A Bayesian Conjugate Gradient Method"

TL;DR

This paper discusses the Bayesian conjugate gradient method, emphasizing prior choices and extending the algorithm to solve multiple related linear systems simultaneously, contributing to probabilistic numerical methods.

Contribution

It introduces an extension of the Bayesian conjugate gradient algorithm for solving multiple related linear systems at once, enhancing its applicability.

Findings

Proposes a new extension of BayesCG for multiple systems

Highlights importance of prior selection in Bayesian linear solvers

Contributes to the development of probabilistic numerical methods

Abstract

We would like to congratulate the authors of "A Bayesian Conjugate Gradient Method" on their insightful paper, and welcome this publication which we firmly believe will become a fundamental contribution to the growing field of probabilistic numerical methods and in particular the sub-field of Bayesian numerical methods. In this short piece, which will be published as a comment alongside the main paper, we first initiate a discussion on the choice of priors for solving linear systems, then propose an extension of the Bayesian conjugate gradient (BayesCG) algorithm for solving several related linear systems simultaneously.