@article{bil-08-aa-hiorder, author = {Giuseppe Bilotta}, title = {Self-Verified Extension of Affine Arithmetic to Arbitrary Order}, journal = {Le Matematiche}, volume = {63}, year = 2008, number = {1}, pages = {15--30}, url = {https://lematematiche.dmi.unict.it/index.php/lematematiche/article/download/47/46}, note = {See errata (missing references)~\cite{bil-08-aa-hiorder-errata}}, comment = {Multilinear AA to approximate multivariate polynomials}, abstract = {Affine Arithmetic (AA) is a self-verifying computational approach that keeps track of first-order correlation between uncertainties in the data and intermediate and final results. In this paper we propose a higher-order extension satisfying the requirements of genericity, arbitrary-order and self-verification, comparing the resulting method with other well-known high-order extensions of AA.} }