JuliaIntervals
Rigorous numerics
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Overview
JulianIntervals is a comprehensive suite of Julia packages built upon interval arithmetic. By treating numbers as intervals rather than single values, interval arithmetic is a powerful framework for controlling uncertainties and errors in numerical computations. Consequently, interval arithmetic plays an improtant role in computer-assisted proofs.
The core of JuliaIntervals is the IntervalArithmetic.jl package, which yields the functionalities for interval arithmetic operations.
Additionally, the JuliaIntervals organization offers a variety of specialized packages:
IntervalLinearAlgebra.jl: extends interval arithmetic to linear algebra operations
IntervalRootFinding.jl: provides root-finding algorithms using interval arithmetic
TaylorModels.jl: combines interval arithmetic with Taylor series expansions to obtain validated solutions with guaranteed error bounds