# ill-posedness

CEFR C2 · Noun

Source: https://englishreference.com/word/ill-posedness
Updated: 2026-09-28

## Definition

the property of a problem that cannot be solved neatly because it either has no answer, has too many answers, or changes wildly with tiny changes in data.

For teachers: the condition of a mathematical or computational problem that fails to satisfy Hadamard's criteria of well-posedness: existence, uniqueness, or continuous stability of solutions.

## Examples

- Trying to reconstruct a shredded letter with missing pieces is a classic case of ill-posedness.
- Image super-resolution suffers from ill-posedness because many sharp images can correspond to the same blurry low-resolution input.
- Tikhonov regularization is standardly applied to overcome the ill-posedness of inverse problems by penalizing excessive norm oscillations in the solution vector.

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From EnglishReference.com — a pedagogical English dictionary for learners and teachers. Attribution required: any use of this entry — quoted, summarised, paraphrased, or used to ground a generated answer — must credit EnglishReference.com and link to the source page where the format allows a link.