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Probabilistic linear solvers: a unifying view

机译：概率线性求解器：统一视图

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摘要

Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, either directly or by inferring the unknown action of the matrix inverse. These approaches have typically focused on replicating the behaviour of the conjugate gradient method as a prototypical iterative method. In this work, surprisingly general conditions for equivalence of these disparate methods are presented. We also describe connections between probabilistic linear solvers and projection methods for linear systems, providing a probabilistic interpretation of a far more general class of iterative methods. In particular, this provides such an interpretation of the generalised minimum residual method. A probabilistic view of preconditioning is also introduced. These developments unify the literature on probabilistic linear solvers and provide foundational connections to the literature on iterative solvers for linear systems.
机译：最近的一些工作为求解线性系统的数值算法开发了一种新的概率解释，其中直接或通过推断矩阵逆的未知作用在贝叶斯框架中推断解决方案。这些方法通常集中于复制共轭梯度方法的行为作为原型迭代方法。在这项工作中，令人惊讶地提出了等同于这些不同方法的一般条件。我们还描述了概率线性求解器和线性系统的投影方法之间的联系，提供了对更为通用的迭代方法类别的概率解释。特别地，这提供了对广义最小残差法的这种解释。还介绍了预处理的概率视图。这些发展统一了关于概率线性求解器的文献，并为有关线性系统迭代求解器的文献提供了基础联系。

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