Conditioning refers to how sensitive a linear system’s output is to small changes in its inputs or parameters. It essentially tells us how well the system can “handle” small perturbations.
Ill-conditioned:
- Characteristics: Even tiny changes to the system can lead to significantly large differences in the final results.
- Analogy: Think of it like a wobbly table. A slight bump can make everything on it fall over.
- Feeling: Unstable and highly sensitive.
Well-conditioned:
- Characteristics: Small changes to the system result in minimal or no change in the final results.
- Analogy: This is like a sturdy table. A slight bump won’t disturb anything on it.
- Feeling: Robust and stable.
In essence, the “condition” of a system describes its ability to withstand external shocks or small changes.
(Meyer, 2000, p. 33)
Reference
Meyer, C. D. (2000). Matrix Analysis and Applied Linear Algebra (Vol. 71). SIAM.