Editing Numerical analysis (section)

===Numerical stability and well-posed problems===
An algorithm is called ''[[numerically stable]]'' if an error, whatever its cause, does not grow to be much larger during the calculation.<ref name="stab">{{harvnb|Higham|2002}}</ref> This happens if the problem is ''[[well-conditioned]]'', meaning that the solution changes by only a small amount if the problem data are changed by a small amount.<ref name="stab"/> To the contrary, if a problem is 'ill-conditioned', then any small error in the data will grow to be a large error.<ref name="stab"/>
Both the original problem and the algorithm used to solve that problem can be well-conditioned or ill-conditioned, and any combination is possible.
So an algorithm that solves a well-conditioned problem may be either numerically stable or numerically unstable. An art of numerical analysis is to find a stable algorithm for solving a well-posed mathematical problem.