The Bayesian Conjugate Gradient method (BayesCG) is a probabilistic generalization of the Conjugate Gradient method (CG) for solving linear systems with real symmetric positive definite coefficient matrices. We present a CG-based implementation of BayesCG with a structure-exploiting prior distribution. The BayesCG output consists of CG iterates and posterior covariances that can be propagated to subsequent computations. The covariances are low-rank and maintained in factored form. This allows easy generation of accurate samples to probe uncertainty in subsequent computations. Numerical experiments confirm the effectiveness of the posteriors and their low-rank approximations.
翻译：Bayesian Conjuge Gradient 方法(Bayesian Conjuge Gradient 方法)是用于用实正对正确定系数矩阵解决线性系统的共振梯度法的概率性一般法。我们介绍了基于CG的BayesCG实施过程,其结构利用了先前的分布。BayesCG产出由CG的外延和后继变量组成,可以传播到随后的计算中。常数是低位的,以系数形式保持。这样可以轻松生成准确的样本,在随后的计算中探测不确定性。数字实验证实了后继器及其低级近似值的有效性。
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