ill-posed.

Failing to have a solution that exists, is unique, and depends continuously on the problem's data.

Use it for

Words that belong together

• ill-posed inverse problem
• ill-posed equation
• ill-posed reconstruction

On the page

Recovering every detail of the original image from the blurred photograph is ill-posed.

The paper adds constraints to make the ill-posed reconstruction more manageable.

Usage notes

Primary category: academic / formal / analytical. Lexical Type: Word. Forms: Normally non-gradable; no ordinary comparative or superlative. Commonness: uncommon (editorial estimate; not a corpus frequency statistic). Legacy lexical fields mirror sense 1; numbered fields keep each relevant meaning separate. Research distinction: Cornell numerical-analysis lecture directly read: well-posed requires existence, uniqueness and continuous dependence on data; failure of any condition is ill-posed. Image reconstruction illustrates possible loss of uniqueness. Source explicitly separates well-posedness from practical conditioning. Individually useful in research, criticism, methodology or conceptual analysis. Definitions and examples are original; no mood or intensity assigned to neutral analytical concepts. Commonness is an editorial estimate, not a frequency statistic. Writing functions: limits on reconstruction from data, lack of existence or uniqueness in a mathematical problem.