{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:14:58Z","timestamp":1760235298103,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,8,15]],"date-time":"2021-08-15T00:00:00Z","timestamp":1628985600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Informatics"],"abstract":"<jats:p>A first aim of the present work is the determination of the actual sources of the \u201cfinite precision error\u201d generation and accumulation in two important algorithms: Bernoulli\u2019s map and the folded Baker\u2019s map. These two computational schemes attract the attention of a growing number of researchers, in connection with a wide range of applications. However, both Bernoulli\u2019s and Baker\u2019s maps, when implemented in a contemporary computing machine, suffer from a very serious numerical error due to the finite word length. This error, causally, causes a failure of these two algorithms after a relatively very small number of iterations. In the present manuscript, novel methods for eliminating this numerical error are presented. In fact, the introduced approach succeeds in executing the Bernoulli\u2019s map and the folded Baker\u2019s map in a computing machine for many hundreds of thousands of iterations, offering results practically free of finite precision error. These successful techniques are based on the determination and understanding of the substantial sources of finite precision (round-off) error, which is generated and accumulated in these two important chaotic maps.<\/jats:p>","DOI":"10.3390\/informatics8030054","type":"journal-article","created":{"date-parts":[[2021,8,15]],"date-time":"2021-08-15T22:51:27Z","timestamp":1629067887000},"page":"54","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Exact Analysis of the Finite Precision Error Generated in Important Chaotic Maps and Complete Numerical Remedy of These Schemes"],"prefix":"10.3390","volume":"8","author":[{"given":"Constantinos","family":"Chalatsis","sequence":"first","affiliation":[{"name":"School of Electrical & Computer Engineering, National Technical University of Athens, Iroon Polytechniou 9, Zografou, 15780 Athens, Greece"}]},{"given":"Constantin","family":"Papaodysseus","sequence":"additional","affiliation":[{"name":"School of Electrical & Computer Engineering, National Technical University of Athens, Iroon Polytechniou 9, Zografou, 15780 Athens, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8438-0471","authenticated-orcid":false,"given":"Dimitris","family":"Arabadjis","sequence":"additional","affiliation":[{"name":"School of Engineering, University of West Attica, Petrou Ralli & Thivon 250 Egaleo, 12241 Athens, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9927-9918","authenticated-orcid":false,"given":"Athanasios Rafail","family":"Mamatsis","sequence":"additional","affiliation":[{"name":"School of Electrical & Computer Engineering, National Technical University of Athens, Iroon Polytechniou 9, Zografou, 15780 Athens, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1367-9564","authenticated-orcid":false,"given":"Nikolaos V.","family":"Karadimas","sequence":"additional","affiliation":[{"name":"Division of Mathematics and Engineering Science, Department of Military Science, Hellenic Army Academy, Evelpidon Avenue, 16672 Vari, Greece"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,15]]},"reference":[{"key":"ref_1","unstructured":"Selvam, A.M. 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Performance Analysis of Chaotic Map Algorithms Comparison of efficiency of Line Map, Bakers and Cat Algorithmfor image cryptography. Proceedings of the 2018 Fourteenth International Conference on Information Processing (ICINPRO), Bangalore, India.","DOI":"10.1109\/ICINPRO43533.2018.9096689"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/S0016-0032(00)00087-9","article-title":"Use of chaotic dynamical systems in cryptography","volume":"338","author":"Schmitz","year":"2001","journal-title":"J. Frankl. Inst."}],"container-title":["Informatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2227-9709\/8\/3\/54\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:46:36Z","timestamp":1760165196000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2227-9709\/8\/3\/54"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,15]]},"references-count":12,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["informatics8030054"],"URL":"https:\/\/doi.org\/10.3390\/informatics8030054","relation":{},"ISSN":["2227-9709"],"issn-type":[{"type":"electronic","value":"2227-9709"}],"subject":[],"published":{"date-parts":[[2021,8,15]]}}}