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The International Centre for Mathematical Sciences (ICMS)

Validated numerics, rooted in Moore’s interval analysis, uses the arithmetic of real intervals to rigorously bound nonlinear functions and control floating-point errors in computations. These methods extend naturally to higher-dimensional and function spaces, forming the basis of rigorous numerical functional analysis. Combined with set-oriented techniques, validated numerics has enabled computer-assisted proofs to address a variety of problems in dynamical systems. Recent advances in computing, and wider availability of platforms that provide support, have led to a resurgence of research activity in the field of validated numerics (and application to computer-assisted proofs).