# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1908.02964