“An ill posed problem is one which doesn’t meet the three Hadamard criteria for being well-posed. These criteria are:” (“Ill Posed Problem: Definition,” Statistics How To, retrieved 6/4/2020)
- “a solution exists,
- “the solution is unique,
- “the solution’s behaviour changes continuously with the initial conditions*” (“Well-posed problem,” Wikipedia, retrieved 6/4/2020)
If the problem does match all three of those criteria, it is considered to be a “well-posed” problem. (ibid.)
“Even if a problem is well-posed, it may still be ill-conditioned, meaning that a small error in the initial data can result in much larger errors in the answers.” (ibid.)
Other sources:
- “ill-posed problem,” The Free Dictionary, retrieved 6/4/2020
- “Ill-posed problems,” Encyclopedia of Mathematics, retrieved 6/4/2020
*Small changes to the inputs of the problem result in (relatively) small changes to the output of the problem no matter what inputs you are using. This doesn’t happen if a small change results in a dramatic output, such as with a step function that has an output of 0 if the input is less than 1 and an output of 100 if the input is greater than or equal to 1.
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Disclaimer:
I am not a professional in this field, nor do I claim to know all of the jargon that is typically used in this field. I am not summarizing my sources; I simply read from a variety of websites until I feel like I understand enough about a topic to move on to what I actually wanted to learn. If I am inaccurate in what I say or you know a better, simpler way to explain a concept, I would be happy to hear from you :).
