Word
ill posedness
Definition
n. 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.
n. 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.”
Examples
simple
“Trying to reconstruct a shredded letter with missing pieces is a classic case of ill-posedness.”
contextual
“Image super-resolution suffers from ill-posedness because many sharp images can correspond to the same blurry low-resolution input.”
complex
“Tikhonov regularization is standardly applied to overcome the ill-posedness of inverse problems by penalizing excessive norm oscillations in the solution vector.”
Etymology
Coined by French mathematician Jacques Hadamard in 1902 in his foundational lectures on partial differential equations (problème mal posé).
Etymology adapted from Wiktionary, available under CC BY-SA 4.0.
Domains
Scan code
englishreference.com/q/ill-posedness