Topic summary
Ill-posed problems
Extracted from the Wikipedia article Well-posed problem.
Conditioning
If the problem is well-posed, then it stands a good chance of solution on a computer using a stable algorithm. If it is not well-posed, it needs to be re-formulated for numerical treatment. Typically this involves including additional assumptions, such as smoothness of solution. This process is known as regularization. Tikhonov regularization is one of the most commonly used for regularization of linear ill-posed problems.