A Variant of the Continued Fraction Expansion Algorithm. (2015)

• Record Type: Journal Article
• Authors: Alexandru, Horváth
• Is Part Of: Procedia technology. Volume 19(2015)
• Page Start: 793
• Page End: 798
• Publication Date: 2015
• Subjects: continued fraction -- numerical approximations -- computational number theory; Technology -- Congresses; Technology -- Periodicals; Engineering -- Congresses; Engineering -- Periodicals; Engineering; Technology; Conference proceedings; Periodicals; 605
• DOI: 10.1016/j.protcy.2015.02.113
• Languages: English
• ISSNs: 2212-0173

Abstract

Abstract: In this note we introduce a new algorithm to compute the continued fraction of a real number. The main difference to the classical algorithm is that our algorithm uses only the number itself to be developed in continued fraction in every step of the iteration process, i.e. the number to be developed in continued fraction is not altered during the steps of the iteration process. By this way the cumulative numerical errors of the floating point computations of the traditional algorithm can be avoided.