Interval arithmetic

Interval arithmetic represents uncertain or rounded values as intervals and computes bounds by applying arithmetic operations to those intervals. It encloses every possible result when the input intervals contain the true values and the operations are evaluated with outward rounding.

Interval: A connected set of real numbers bounded by two endpoints. Each quantity is represented by a set of possible values with lower and upper bounds.
Validated numerics: Numerical computation that uses rigorous error bounds to certify results. Interval arithmetic is a standard tool for proving that numerical answers enclose exact ones.
Moore's interval analysis: The systematic development of interval methods for numerical analysis associated with Ramon E. Moore. Moore established interval computation as a framework for rigorous numerical bounds.
Monte Carlo method: A computational method that estimates quantities by repeated random sampling. Sampling estimates typical behavior, while intervals aim to enclose every possible value.
Directed rounding: A floating-point rounding mode that rounds results toward positive or negative infinity. Outward rounding keeps computed endpoints from excluding exact results.
Interval analysis: The mathematical study and application of interval-valued computation and bounds. This broader field develops theory and methods built around interval arithmetic.
Ramon E. Moore: An American mathematician who developed foundational methods in interval analysis. His work shaped the modern mathematical treatment of interval computation.
Probability distribution: A mathematical description of the probabilities assigned to possible values of a random variable. Intervals encode ranges without assigning likelihoods to values.
Interval dependency problem: The overestimation that occurs when interval calculations treat repeated occurrences of the same variable independently. Repeated variables can make propagated bounds wider than the true range.
Global optimization: Optimization methods that seek a global rather than merely local optimum over a domain. Interval bounds can rule out regions that cannot contain a global optimum.

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