Numerical stability
- Category
- STANDARD MATHEMATICS
- Definition
- The tendency of a computation to give essentially the same result under harmless changes of precision, mesh or method.
- Math Level
- TECHNICAL
Numerical stability describes whether a computation gives essentially the same answer when harmless numerical details are changed.
Useful checks include increasing precision, refining a mesh, extending a truncated tail and recomputing by a different representation. Stability increases confidence that an observed feature is not a numerical artefact, but it is not automatically a proof.
See also: numerical precision, mesh size, tail truncation, cross-check.