Fault-tolerant modular reconstruction of rational numbers. (May 2017)

• Record Type: Journal Article
• Authors: Abbott, John
• Is Part Of: Journal of symbolic computation. Volume 80:Part 3(2017)
• Page Start: 707
• Page End: 718
• Publication Date: 2017-05
• Subjects: 11A07 -- 68W30; Fault-tolerant rational reconstruction -- Chinese remaindering; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.07.030
• Languages: English
• ISSNs: 0747-7171

Abstract

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.