A Family of Multiple-Root Finding Iterative Methods Based on Weight Functions
A straightforward family of one-point multiple-root iterative methods is introduced. The family is generated using the technique of weight functions. The order of convergence of the family is determined in its convergence analysis, which shows the constraints that the weight function must satisfy to...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/12/2194 |
| _version_ | 1797545243709538304 |
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| author | Francisco I. Chicharro Rafael A. Contreras Neus Garrido |
| author_facet | Francisco I. Chicharro Rafael A. Contreras Neus Garrido |
| author_sort | Francisco I. Chicharro |
| collection | DOAJ |
| description | A straightforward family of one-point multiple-root iterative methods is introduced. The family is generated using the technique of weight functions. The order of convergence of the family is determined in its convergence analysis, which shows the constraints that the weight function must satisfy to achieve order three. In this sense, a family of iterative methods can be obtained with a suitable design of the weight function. That is, an iterative algorithm that depends on one or more parameters is designed. This family of iterative methods, starting with proper initial estimations, generates a sequence of approximations to the solution of a problem. A dynamical analysis is also included in the manuscript to study the long-term behavior of the family depending on the parameter value and the initial guess considered. This analysis reveals the good properties of the family for a wide range of values of the parameter. In addition, a numerical test on academic and engineering multiple-root functions is performed. |
| first_indexed | 2024-03-10T14:11:45Z |
| format | Article |
| id | doaj.art-798821d1b6b44fc3ac931e633cfdbff8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T14:11:45Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-798821d1b6b44fc3ac931e633cfdbff82023-11-21T00:05:00ZengMDPI AGMathematics2227-73902020-12-01812219410.3390/math8122194A Family of Multiple-Root Finding Iterative Methods Based on Weight FunctionsFrancisco I. Chicharro0Rafael A. Contreras1Neus Garrido2Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de la Rioja, Av. La Paz 137, 26006 Logroño, SpainEscuela Superior de Ingeniería y Tecnología, Universidad Internacional de la Rioja, Av. La Paz 137, 26006 Logroño, SpainEscuela Superior de Ingeniería y Tecnología, Universidad Internacional de la Rioja, Av. La Paz 137, 26006 Logroño, SpainA straightforward family of one-point multiple-root iterative methods is introduced. The family is generated using the technique of weight functions. The order of convergence of the family is determined in its convergence analysis, which shows the constraints that the weight function must satisfy to achieve order three. In this sense, a family of iterative methods can be obtained with a suitable design of the weight function. That is, an iterative algorithm that depends on one or more parameters is designed. This family of iterative methods, starting with proper initial estimations, generates a sequence of approximations to the solution of a problem. A dynamical analysis is also included in the manuscript to study the long-term behavior of the family depending on the parameter value and the initial guess considered. This analysis reveals the good properties of the family for a wide range of values of the parameter. In addition, a numerical test on academic and engineering multiple-root functions is performed.https://www.mdpi.com/2227-7390/8/12/2194multiple-rootsiterative methodweight functioncomplex dynamics |
| spellingShingle | Francisco I. Chicharro Rafael A. Contreras Neus Garrido A Family of Multiple-Root Finding Iterative Methods Based on Weight Functions Mathematics multiple-roots iterative method weight function complex dynamics |
| title | A Family of Multiple-Root Finding Iterative Methods Based on Weight Functions |
| title_full | A Family of Multiple-Root Finding Iterative Methods Based on Weight Functions |
| title_fullStr | A Family of Multiple-Root Finding Iterative Methods Based on Weight Functions |
| title_full_unstemmed | A Family of Multiple-Root Finding Iterative Methods Based on Weight Functions |
| title_short | A Family of Multiple-Root Finding Iterative Methods Based on Weight Functions |
| title_sort | family of multiple root finding iterative methods based on weight functions |
| topic | multiple-roots iterative method weight function complex dynamics |
| url | https://www.mdpi.com/2227-7390/8/12/2194 |
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