Numerical Stability

Numerical Analysis · Axiom Academy

Algorithms that resist error amplification Stability and accuracy are different concepts. An algorithm can be stable but inaccurate, or accurate for exact arithmetic but unstable in floating-point. 2. Forward vs Backward Stability There are two ways to think about stability: Even simple summation can be done stably or unstably. The order of operations matters! Signs that an algorithm may be unstable: Results vary wildly with small input changes Different mathematically equivalent formulas give different answers Results depend on evaluation order Running in higher precision gives very different results

This is the written version of the interactive lesson above. See the full Numerical Analysis course.