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AccuracyGoal

Status: Experimental

present and registered, but lightly documented and not yet covered by dedicated tests.

Description

AccuracyGoal

is an option for numerical operations (NLimit, NSum, NProduct, NIntegrate, NDSolve, NResidue, ND, NSeries, FindRoot, NRoots, NSolve) specifying how many digits of ABSOLUTE accuracy to seek.

Notes With AccuracyGoal -\> a and PrecisionGoal -\> p, Mathilda seeks a result whose numerical error in a value of size x is below 10^-a + |x| 10^-p: a is the absolute term, p the relative term, of the combined tolerance. AccuracyGoal effectively bounds the absolute error. AccuracyGoal -\> MachinePrecision (the default) seeks ~$MachinePrecision (about 15.95) digits. AccuracyGoal -\> Automatic seeks near-full working precision (two digits below WorkingPrecision). AccuracyGoal -\> Infinity disables the absolute criterion, leaving PrecisionGoal to govern termination. Each operation refines adaptively -- growing its term count, sampling, or recursion up to a resource cap -- until the goal is met. If it cannot be met at the cap, a Head::accgl message is issued and the best approximation obtained is returned. Set WorkingPrecision at least as large as AccuracyGoal; otherwise the result may fall well short of it.

Examples

No verified examples yet for this function.

Implementation notes

Attributes: none registered.

References