PosteriorContractionStoppingCriterion

class probnum.linalg.solvers.stopping_criteria.PosteriorContractionStoppingCriterion(qoi='x', atol=1e-05, rtol=1e-05)

Bases: LinearSolverStoppingCriterion

Posterior contraction stopping criterion.

Terminate when the uncertainty about the quantity of interest \(q\) is sufficiently small, i.e. if \(\sqrt{\operatorname{tr}(\mathbb{Cov}(q))} \leq \max(\text{atol}, \text{rtol} \lVert b \rVert_2)\), where \(q\) is either the solution \(x\), the system matrix \(A\) or its inverse \(A^{-1}\).

Parameters

• qoi (str) – Quantity of interest. One of {"x", "A", "Ainv"}.

• atol (Union[int, float, complex, Number, number]) – Absolute tolerance.

• rtol (Union[int, float, complex, Number, number]) – Relative tolerance.

Methods Summary

__call__(solver_state)

Check whether the uncertainty about the quantity of interest is smaller than the specified tolerance.

Methods Documentation

__call__(solver_state)

Check whether the uncertainty about the quantity of interest is smaller than the specified tolerance.

Parameters

solver_state (LinearSolverState) – Current state of the linear solver.

Return type

bool