What does 'numerical stability' refer to in computational methods?

Numerical stability refers to the characteristic of an algorithm that ensures it can produce bounded errors throughout the computational process. This concept is crucial in numerical analysis as it addresses how small changes in input or rounding errors during calculations can affect the final output. An algorithm is considered numerically stable if these errors do not grow uncontrollably, allowing the results to remain reliable and accurate under various conditions.

This concept is especially important when dealing with iterative methods, where small errors can propagate and potentially lead to significant deviations from the expected result. A numerically stable method can help maintain the integrity of results even when the calculations involve operations that are sensitive to such errors. In contrast, options discussing operational efficiency or speed do not capture the essence of what numerical stability entails, as those aspects are more about performance rather than the integrity and reliability of the results.