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A note on the convergence of the secant method for simple and multiple roots
| dc.contributor.author | Díez, Pedro |
| dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III |
| dc.date.accessioned | 2010-07-29T14:53:06Z |
| dc.date.available | 2010-07-29T14:53:06Z |
| dc.date.created | 2003-11 |
| dc.date.issued | 2003-11 |
| dc.identifier.citation | Díez, P. A note on the convergence of the secant method for simple and multiple roots. "Applied mathematics letters", Novembre 2003, vol. 16, núm. 8, p. 1211-1215. |
| dc.identifier.issn | 0893-9659 |
| dc.identifier.uri | http://hdl.handle.net/2117/8459 |
| dc.description.abstract | The secant method is one of the most popular methods for root finding. Standard text books in numerical analysis state that the secant method is super linear: the rate of convergence is set by the gold number. Never- theless, this property holds only for simple roots. If the multiplicity of the root is larger than one, the convergence of the secant method becomes linear. This communication includes a detailed analysis of the secant method when it is used to approximate multiple roots. Thus, a proof of the linear convergence is shown. Moreover, the values of the corresponding asymptotic convergence factors are determined and are found to be also related with the golden ratio. |
| dc.format.extent | 5 p. |
| dc.language.iso | eng |
| dc.publisher | Elsevier |
| dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica |
| dc.subject.lcsh | Numerical analysis |
| dc.subject.other | Secant method |
| dc.subject.other | Convergence rate |
| dc.subject.other | Asymptotic behavior |
| dc.title | A note on the convergence of the secant method for simple and multiple roots |
| dc.type | Article |
| dc.subject.lemac | Anàlisi numèrica |
| dc.contributor.group | Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
| dc.identifier.doi | 10.1016/S0893-9659(03)90119-4 |
| dc.description.peerreviewed | Peer Reviewed |
| dc.rights.access | Open Access |
| local.identifier.drac | 772556 |
| dc.description.version | Postprint (author’s final draft) |
| local.citation.author | Díez, P. |
| local.citation.publicationName | Applied mathematics letters |
| local.citation.volume | 16 |
| local.citation.number | 8 |
| local.citation.startingPage | 1211 |
| local.citation.endingPage | 1215 |
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