Numerical stability

Numerical stability refers to how well a computational process handles small errors or uncertainties during calculations. When a calculation is stable, these tiny inaccuracies don't grow significantly, ensuring the final result remains accurate and reliable. Conversely, unstable algorithms can amplify small errors, leading to incorrect results even if the initial data is precise. Stability is crucial in numerical methods because it determines whether the calculations are robust against the inevitable small mistakes that occur in computer computations. Essentially, a numerically stable process maintains accuracy despite minor imperfections or rounding errors.