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Validated numerics
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<p> Validated numerics, or rigorous computation, verified computation, reliable computation, numerical verification is numerics including mathematically strict error (rounding error, truncation error, discretization error) evaluation, and it is one field of <a href="/facts/Numerical_analysis/QT9cYa9z">numerical analysis</a>. For computation, <a href="/facts/Interval_arithmetic/1ylnKraf">interval arithmetic</a> is most often used, where all results are represented by intervals. Validated numerics were used by <a href="/facts/Warwick_Tucker/w47LIMUT">Warwick Tucker</a> in order to solve the 14th of <a href="/facts/Smale%2527s_problems/Lep2Fld4">Smale's problems</a>, and today it is recognized as a powerful tool for the study of <a href="/facts/Dynamical_systems/782gREl5">dynamical systems</a>. </p>