Convergence
- Category
- STANDARD MATHEMATICS
- Definition
- The approach of a sequence of approximations toward a definite limiting value as the approximation is refined.
- Math Level
- TECHNICAL
Convergence means that a sequence of approximations approaches a definite limiting value as the approximation is refined.
In numerical work one may refine a mesh, increase a cutoff or raise precision and look for the computed result to settle. Apparent convergence is valuable evidence, but a rigorous proof of convergence may require explicit mathematical error bounds.
See also: mesh size, tail truncation, numerical stability, proof.