Katastrofy

In computer science, „katastrofy“ (or „catastrophic cancellation“) refers to a numerical issue that occurs when subtracting two nearly equal numbers, leading to a significant loss of precision in the result. This phenomenon arises due to the limitations of floating-point arithmetic, where the significant digits of the values are lost in the operation, resulting in a value that is less accurate than expected. For example, when computing ( a – b ) where ( a ) and ( b ) are very close in value, the significant digits can cancel out, yielding a result that may appear to be correct at first glance but is actually unreliable. Catastrophic cancellation is a critical consideration in numerical analysis and computational algorithms, as it can lead to erroneous outcomes if not managed properly. Techniques such as reformulating equations, using higher precision data types, or employing special algorithms are often employed to mitigate its effects and ensure numerical stability.