Stopping criterion based on relative error reduction




  • Alias: None

  • Arguments: REAL

  • Default: 1.e-4


The convergence_tolerance specification provides a real value for controlling the termination of iteration through satisfaction of a specified accuracy at minimum total cost.

For multilevel and multifidelity sampling methods, it is a relative convergence tolerance on the mean squared error (MSE), where the MSE is typically comprised of known estimator variance (stochastic error), neglecting unknown residual bias (deterministic error).

The reference estimator variance is then defined as follows:

  • Multilevel approaches ( multilevel_sampling and multilevel_multifidelity_sampling): tolerance relative to initial multilevel Monte Carlo (MLMC) error after pilot sample

  • Control variate approaches ( multifidelity_sampling and approximate_control_variate): relative to Monte Carlo (MC) error from pilot sample where these are all initial estimator variances fot the algorithm, recognizing that control variate approaches can extract no benefit from low-fidelity pilot samples prior to the definition of corresponding sample increments.

Permissible values are between 0 and 1, non-inclusive. Default value is 1.e-4.