Fault-tolerant modular reconstruction of rational numbers

In this paper we present two efficient methods for reconstructing a rational number from several residue-modulus pairs, some of which may be incorrect. One method is a natural generalization of that presented by Wang et al. in (Wang et al., 1982) (for reconstructing a rational number from correct modular images), and also of an algorithm presented in Abbott (1991) for reconstructing an integer value from several residue-modulus pairs, some of which may be incorrect. The other method is heuristic, but much easier to apply; it may be viewed as a generalization of Monagan's MQRR (Monagan, 2004). We compare our heuristic method with that of Bohm et al. (2015). Our method is clearly preferable when the rational to be reconstructed is unbalanced. (C) 2016 Elsevier Ltd. All rights reserved.