Exact Analysis of the Finite Precision Error Generated in Important Chaotic Maps and Complete Numerical Remedy of These Schemes
A first aim of the present work is the determination of the actual sources of the “finite precision error” generation and accumulation in two important algorithms: Bernoulli’s map and the folded Baker’s map. These two computational schemes attract the attention of a growing number of researchers, in...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-08-01
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| Series: | Informatics |
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| Online Access: | https://www.mdpi.com/2227-9709/8/3/54 |
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| author | Constantinos Chalatsis Constantin Papaodysseus Dimitris Arabadjis Athanasios Rafail Mamatsis Nikolaos V. Karadimas |
| author_facet | Constantinos Chalatsis Constantin Papaodysseus Dimitris Arabadjis Athanasios Rafail Mamatsis Nikolaos V. Karadimas |
| author_sort | Constantinos Chalatsis |
| collection | DOAJ |
| description | A first aim of the present work is the determination of the actual sources of the “finite precision error” generation and accumulation in two important algorithms: Bernoulli’s map and the folded Baker’s 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’s and Baker’s 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’s map and the folded Baker’s 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. |
| first_indexed | 2024-03-10T07:34:30Z |
| format | Article |
| id | doaj.art-15e96af268f841218b0cfca17b96d3c5 |
| institution | Directory Open Access Journal |
| issn | 2227-9709 |
| language | English |
| last_indexed | 2024-03-10T07:34:30Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Informatics |
| spelling | doaj.art-15e96af268f841218b0cfca17b96d3c52023-11-22T13:34:50ZengMDPI AGInformatics2227-97092021-08-01835410.3390/informatics8030054Exact Analysis of the Finite Precision Error Generated in Important Chaotic Maps and Complete Numerical Remedy of These SchemesConstantinos Chalatsis0Constantin Papaodysseus1Dimitris Arabadjis2Athanasios Rafail Mamatsis3Nikolaos V. Karadimas4School of Electrical & Computer Engineering, National Technical University of Athens, Iroon Polytechniou 9, Zografou, 15780 Athens, GreeceSchool of Electrical & Computer Engineering, National Technical University of Athens, Iroon Polytechniou 9, Zografou, 15780 Athens, GreeceSchool of Engineering, University of West Attica, Petrou Ralli & Thivon 250 Egaleo, 12241 Athens, GreeceSchool of Electrical & Computer Engineering, National Technical University of Athens, Iroon Polytechniou 9, Zografou, 15780 Athens, GreeceDivision of Mathematics and Engineering Science, Department of Military Science, Hellenic Army Academy, Evelpidon Avenue, 16672 Vari, GreeceA first aim of the present work is the determination of the actual sources of the “finite precision error” generation and accumulation in two important algorithms: Bernoulli’s map and the folded Baker’s 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’s and Baker’s 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’s map and the folded Baker’s 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.https://www.mdpi.com/2227-9709/8/3/54finite precision error generationfinite precision error accumulationstabilization of algorithmsstable Bernoulli’s mapstable Baker’s map |
| spellingShingle | Constantinos Chalatsis Constantin Papaodysseus Dimitris Arabadjis Athanasios Rafail Mamatsis Nikolaos V. Karadimas Exact Analysis of the Finite Precision Error Generated in Important Chaotic Maps and Complete Numerical Remedy of These Schemes Informatics finite precision error generation finite precision error accumulation stabilization of algorithms stable Bernoulli’s map stable Baker’s map |
| title | Exact Analysis of the Finite Precision Error Generated in Important Chaotic Maps and Complete Numerical Remedy of These Schemes |
| title_full | Exact Analysis of the Finite Precision Error Generated in Important Chaotic Maps and Complete Numerical Remedy of These Schemes |
| title_fullStr | Exact Analysis of the Finite Precision Error Generated in Important Chaotic Maps and Complete Numerical Remedy of These Schemes |
| title_full_unstemmed | Exact Analysis of the Finite Precision Error Generated in Important Chaotic Maps and Complete Numerical Remedy of These Schemes |
| title_short | Exact Analysis of the Finite Precision Error Generated in Important Chaotic Maps and Complete Numerical Remedy of These Schemes |
| title_sort | exact analysis of the finite precision error generated in important chaotic maps and complete numerical remedy of these schemes |
| topic | finite precision error generation finite precision error accumulation stabilization of algorithms stable Bernoulli’s map stable Baker’s map |
| url | https://www.mdpi.com/2227-9709/8/3/54 |
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