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The study of the propagation of errors in a numerical algorithm.

Numerical algorithms often make a sequence of approximations that should converge to the "correct solution" in the limit sense. However, due to issues such as finite precision or algorithmic implementation, small initial errors can be magnified quickly to produce an answer that does not satisfy our expected tolerance. This is of particular interest to numerical solutions of differential and partial differential equations, but is not limited to these fields. Subtraction of nearly equal quantities tends to be a common cause of numerical instability, but may not be the only source of instability.