# ProbabilisticLinearSolver¶

class probnum.linalg.solvers.ProbabilisticLinearSolver

Bases: object

Compose a custom probabilistic linear solver.

Class implementing probabilistic linear solvers. Such (iterative) solvers infer solutions to problems of the form

$Ax=b,$

where $$A \in \mathbb{R}^{n \times n}$$ and $$b \in \mathbb{R}^{n}$$. They return a probability measure which quantifies uncertainty in the output arising from finite computational resources or stochastic input. This class unifies and generalizes probabilistic linear solvers as described in the literature. 1 2 3 4

References

1

Hennig, P., Probabilistic Interpretation of Linear Solvers, SIAM Journal on Optimization, 2015, 25, 234-260

2

Cockayne, J. et al., A Bayesian Conjugate Gradient Method, Bayesian Analysis, 2019, 14, 937-1012

3

Bartels, S. et al., Probabilistic Linear Solvers: A Unifying View, Statistics and Computing, 2019

4

Wenger, J. and Hennig, P., Probabilistic Linear Solvers for Machine Learning, Advances in Neural Information Processing Systems (NeurIPS), 2020

problinsolve
bayescg