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{{Draft article}}
'''Numerical certification''' is the process of verifying the correctness of a candidate solution to a system of equations, often a result of algorithmic calculation. In numerical computational mathematics, such as [[numerical algebraic geometry]], candidate solutions are computed, but there is the possibility that errors have been introduced. Beyond the inexactness of candidates, they may also simply be grossly incorrect as the result of any of a
Methods for certification can be divided into two flavors: ''a priori'' certification and ''a posteriori'' certification. ''A posteriori'' certification confirms the correctness of the final answers (regardless of how they are generated) while ''a priori'' certification confirms the correctness of each step of a specific computation. A typical example of ''a posteriori'' certification is [[Stephen_Smale|Smale]]'s alpha theory, while a typical example of ''a priori'' certification is [[interval arithmetic]].
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