Fault-tolerant modular reconstruction of rational numbers. (May 2017) - Abbott, John
Abstract: 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 Böhm et al. (2015) . Our method is clearly preferable when the rational to be reconstructed is unbalanced.