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We completely describe a new domain for abstract interpretation of numericalprograms. Fixpoint iteration in this domain is proved to converge to finiteprecise invariants for (at least) the class of stable linear recursive filtersof any order. Good evidence shows it behaves well also for some non-linearschemes. The result, and the structure of the domain, rely on an interestinginterplay between order and topology.

Perturbed affine arithmetic for invariant computation in numerical program analysis