# Well Posedness: Simple Definition for Well-Posed

The well posedness of a problem refers to whether or not the problem is stable, as determined by whether it meets the three Hadamard criteria, which tests whether or not the problem has:

1. A solution: s exists for all d (for every d relevant to the problem).
2. A unique solution: s is unique for all d; for every data point d there is at most one value of s.
3. A stable solution: s depends continously on d (a tiny change in d will lead to a tiny change in s; and a large change in d will lead to a proportionally larger change in s).

The Hadamard criteria tells us how well a problem lends itself to mathematical analysis.

------------------------------------------------------------------------------

Need help with a homework or test question? With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. Your first 30 minutes with a Chegg tutor is free!

Statistical concepts explained visually - Includes many concepts such as sample size, hypothesis tests, or logistic regression, explained by Stephanie Glen, founder of StatisticsHowTo.