reapproximated

Reapproximated is the past participle of reapproximate, meaning to obtain or provide another approximation of a value, function, or model after receiving new information, refinement of methods, or changes in available data. It is used mainly in mathematical, computational, and statistical contexts to describe iterative refinement rather than a transition to an exact solution.

In numerical analysis and computation, reapproximation occurs when an algorithm revises a previous estimate using updated procedures, higher precision, or alternative representations. For example, after an initial root or solution is found, a solver may reapproximate the result with a higher-order method or a different numerical basis to reduce error bounds or improve stability.

In statistics and data analysis, reapproximation can refer to updating an approximation of a distribution, likelihood, or posterior when new data arrive or when a model is altered. Techniques such as variational approximation or Laplace approximations may be revised or refined, effectively reapproximating the target quantity.

In geometry, computer graphics, and data assimilation, reapproximation often involves replacing or adjusting a curve, surface, or trajectory with a new approximation that better fits observed data or satisfies additional constraints. This may entail changing control points, basis functions, or parameterizations.

While the term is informal and context-dependent, reapproximated values generally signal iterative improvement rather than final exactness. It is common to specify the method, data, or basis used in the reapproximation to clarify the refinement process.