An Introduction to Affine Arithmetic

J. Stolfi, L.H. de Figueiredo


Affine arithmetic (AA) is a model for self-validated computation which, like standard interval arithmetic (IA), produces guaranteed enclosures for computed quantities, taking into account any uncertainties in the input data as well as all internal truncation and roundoff errors. Unlike standard IA, the quantity representations used by AA are first-order approximations, whose error is generally quadratic in the width of input intervals. In many practical applications, the higher asymptotic accuracy of AA more than compensates for the increased cost of its operations.


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