Conditioning (Numerical Methods)

I was introduced to this briefly in CS370.

Conditioning describes how the output of a function/operation/problem changes due to changes in input.

Conditioning is indicative of how difficult a problem is to solve, independent of the algorithm / numerical method used.

Norms are useful in understanding linear system conditioning.

For a given perturbation, we say the system is

• Well-conditioned if $x$ changes little
• Ill-conditioned if $x$ changes lots.