Glossary

Conditioning

Sensitivity of the exact problem to perturbations in the data.

Definition

Conditioning belongs to the problem, not to the algorithm. In linear systems it is measured by $\kappa(A)=\|A\|\,\|A^{-1}\|$ : if large, small errors in $A$ or $b$ can cause large errors in $x$ .

How it is used

It separates a poor algorithm from an intrinsically sensitive problem: changing algorithms does not remove ill-conditioning.