Editing Well-posed problem (section)

==Conditioning==
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. Problems in nonlinear [[complex systems]] (so-called [[Chaos theory|chaotic]] systems) provide well-known examples of instability. An ill-conditioned problem is indicated by a large [[condition number]].

If the problem is well-posed, then it stands a good chance of solution on a computer using a [[numerical stability|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 (mathematics)|regularization]]''.<ref>{{cite journal | last1 = Huang | first1 = Yunfei. | display-authors = etal | year = 2019 | title = Traction force microscopy with optimized regularization and automated Bayesian parameter selection for comparing cells | journal = Scientific Reports | volume = 9 | number = 1| page = 537 | doi = 10.1038/s41598-018-36896-x | pmid = 30679578 | doi-access = free | pmc = 6345967 | arxiv = 1810.05848 | bibcode = 2019NatSR...9..539H }}</ref>  [[Tikhonov regularization]] is one of the most commonly used for regularization of linear ill-posed problems.