Halving interval guaranteed for Dekker and Brent root finding methods
Hybrid methods are widely used in many areas of applied mathematics. One of the simplest and most common problems in this field is root finding, for which various methods exist. Some of the most efficient approaches combine two or more techniques into hybrid methods. Among these are the Dekker and B...
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| Language: | English |
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Elsevier
2025-06-01
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| Series: | Examples and Counterexamples |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666657X24000399 |
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| author | Vilmar Steffen Carlos Catusso Della Pasqua Maiquiel Schmidt de Oliveira Edson Antonio da Silva |
| author_facet | Vilmar Steffen Carlos Catusso Della Pasqua Maiquiel Schmidt de Oliveira Edson Antonio da Silva |
| author_sort | Vilmar Steffen |
| collection | DOAJ |
| description | Hybrid methods are widely used in many areas of applied mathematics. One of the simplest and most common problems in this field is root finding, for which various methods exist. Some of the most efficient approaches combine two or more techniques into hybrid methods. Among these are the Dekker and Brent methods, for which we propose a modification to ensure that the search interval is halved in each iteration. We apply this modification to two examples: a transcendental equation and a cubic equation of state. The results demonstrate that the proposed modifications guarantee at least interval halving and offer a slight improvement in the efficiency of the root-finding process. |
| format | Article |
| id | doaj-art-a8134d3ce3704ac18325ada61bd9a691 |
| institution | DOAJ |
| issn | 2666-657X |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Examples and Counterexamples |
| spelling | doaj-art-a8134d3ce3704ac18325ada61bd9a6912025-08-20T03:21:38ZengElsevierExamples and Counterexamples2666-657X2025-06-01710017310.1016/j.exco.2024.100173Halving interval guaranteed for Dekker and Brent root finding methodsVilmar Steffen0Carlos Catusso Della Pasqua1Maiquiel Schmidt de Oliveira2Edson Antonio da Silva3Academic Departments of Engineering (DAENG), Federal University of Technology - Parana (UTFPR), Rua Gelindo Joao Folador, 2000, Francisco Beltrao, 85602-863, Parana, Brazil; Postgraduate Program in Chemical Engineering, State University of Paraná (Unioeste), Rua da Faculdade, 645, Toledo, 85903-000, Parana, Brazil; Corresponding author at: Academic Departments of Engineering (DAENG), Federal University of Technology - Parana (UTFPR), Rua Gelindo Joao Folador, 2000, Francisco Beltrao, 85602-863, Parana, Brazil.Chemical Engineering Corse, Federal University of Technology - Parana (UTFPR), Rua Gelindo Joao Folador, 2000, Francisco Beltrao, 85602-863, Parana, BrazilAcademic Department of Physics, Statistics and Mathematics (DAFEM), Federal University of Technology - Parana (UTFPR), Rua Gelindo Joao Folador, 2000, Francisco Beltrao, 85602-863, Parana, BrazilCenter for Engineering and Exact Sciences (CECE), State University of Paraná (Unioeste), Rua da Faculdade, 645, Toledo, 85903-000, Parana, Brazil; Postgraduate Program in Chemical Engineering, State University of Paraná (Unioeste), Rua da Faculdade, 645, Toledo, 85903-000, Parana, BrazilHybrid methods are widely used in many areas of applied mathematics. One of the simplest and most common problems in this field is root finding, for which various methods exist. Some of the most efficient approaches combine two or more techniques into hybrid methods. Among these are the Dekker and Brent methods, for which we propose a modification to ensure that the search interval is halved in each iteration. We apply this modification to two examples: a transcendental equation and a cubic equation of state. The results demonstrate that the proposed modifications guarantee at least interval halving and offer a slight improvement in the efficiency of the root-finding process.http://www.sciencedirect.com/science/article/pii/S2666657X24000399Root findingInterval halvingDekker methodBrent methodHybrid method |
| spellingShingle | Vilmar Steffen Carlos Catusso Della Pasqua Maiquiel Schmidt de Oliveira Edson Antonio da Silva Halving interval guaranteed for Dekker and Brent root finding methods Examples and Counterexamples Root finding Interval halving Dekker method Brent method Hybrid method |
| title | Halving interval guaranteed for Dekker and Brent root finding methods |
| title_full | Halving interval guaranteed for Dekker and Brent root finding methods |
| title_fullStr | Halving interval guaranteed for Dekker and Brent root finding methods |
| title_full_unstemmed | Halving interval guaranteed for Dekker and Brent root finding methods |
| title_short | Halving interval guaranteed for Dekker and Brent root finding methods |
| title_sort | halving interval guaranteed for dekker and brent root finding methods |
| topic | Root finding Interval halving Dekker method Brent method Hybrid method |
| url | http://www.sciencedirect.com/science/article/pii/S2666657X24000399 |
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