... Krawczyk’s method is well deÿned and x∗∈[x]k;k¿0.If on the other hand f(x) = 0 and K[x]k∩ [x]k= ∅ then {[x]k} is well deÿned. Because of(B) ¡ 1 we have d[x]k→ 0 and since we have a nested ... Today theunderstanding of the theory and the use of adapted programming languages are indispensible toolsfor reliable advanced scientiÿc computing.2. Deÿnitions, notations and basic factsLet ... (Eds.), Validation Numerics, Theory and Applications, Springer,Wien, 1993, pp. 265–285.Further reading[1] G. Alefeld, A. Frommer, B. Lang (Eds.), Scientiÿc Computing and Validated Numerics, Mathematical...