Matches in SemOpenAlex for { <https://semopenalex.org/work/W4287165103> ?p ?o ?g. }
Showing items 1 to 91 of
91
with 100 items per page.
- W4287165103 abstract "The secant method is a very effective numerical procedure used for solving nonlinear equations of the form $f(x)=0$. In a recent work [A. Sidi, Generalization of the secant method for nonlinear equations. {em Appl. Math. E-Notes}, 8:115--123, 2008] we presented a generalization of the secant method that uses only one evaluation of $f(x)$ per iteration, and we provided a local convergence theory for it that concerns real roots. For each integer $k$, this method generates a sequence ${x_n}$ of approximations to a real root of $f(x)$, where, for $ngeq k$, $x_{n+1}=x_n-f(x_n)/p'_{n,k}(x_n)$, $p_{n,k}(x)$ being the polynomial of degree $k$ that interpolates $f(x)$ at $x_n,x_{n-1},ldots,x_{n-k}$, the order $s_k$ of this method satisfying $1<s_k<2$. Clearly, when $k=1$, this method reduces to the secant method with $s_1=(1+sqrt{5})/2$. In addition, $s_1<s_2<s_3<cdots,$ such that and $lim_{ktoinfty}s_k=2$. In this note, we study the application of this method to simple complex roots of a real or complex function $f(z)$. We show that the local convergence theory developed for real roots can be extended almost as is to complex roots, provided suitable assumptions and justifications are made. We illustrate the theory with two numerical examples." @default.
- W4287165103 created "2022-07-25" @default.
- W4287165103 creator A5067073885 @default.
- W4287165103 date "2021-05-28" @default.
- W4287165103 modified "2023-09-24" @default.
- W4287165103 title "Application of a Generalized Secant Method to Nonlinear Equations with Complex Roots" @default.
- W4287165103 doi "https://doi.org/10.48550/arxiv.2105.13748" @default.
- W4287165103 hasPublicationYear "2021" @default.
- W4287165103 type Work @default.
- W4287165103 citedByCount "0" @default.
- W4287165103 crossrefType "posted-content" @default.
- W4287165103 hasAuthorship W4287165103A5067073885 @default.
- W4287165103 hasBestOaLocation W42871651031 @default.
- W4287165103 hasConcept C10138342 @default.
- W4287165103 hasConcept C111472728 @default.
- W4287165103 hasConcept C11413529 @default.
- W4287165103 hasConcept C114614502 @default.
- W4287165103 hasConcept C117898588 @default.
- W4287165103 hasConcept C121332964 @default.
- W4287165103 hasConcept C134306372 @default.
- W4287165103 hasConcept C138885662 @default.
- W4287165103 hasConcept C158622935 @default.
- W4287165103 hasConcept C159694833 @default.
- W4287165103 hasConcept C162324750 @default.
- W4287165103 hasConcept C177148314 @default.
- W4287165103 hasConcept C182306322 @default.
- W4287165103 hasConcept C194777461 @default.
- W4287165103 hasConcept C199360897 @default.
- W4287165103 hasConcept C24890656 @default.
- W4287165103 hasConcept C2775997480 @default.
- W4287165103 hasConcept C2777303404 @default.
- W4287165103 hasConcept C2778112365 @default.
- W4287165103 hasConcept C2780586882 @default.
- W4287165103 hasConcept C28826006 @default.
- W4287165103 hasConcept C33923547 @default.
- W4287165103 hasConcept C41008148 @default.
- W4287165103 hasConcept C50522688 @default.
- W4287165103 hasConcept C54355233 @default.
- W4287165103 hasConcept C62520636 @default.
- W4287165103 hasConcept C85189116 @default.
- W4287165103 hasConcept C86803240 @default.
- W4287165103 hasConcept C90119067 @default.
- W4287165103 hasConcept C93926214 @default.
- W4287165103 hasConcept C97137487 @default.
- W4287165103 hasConceptScore W4287165103C10138342 @default.
- W4287165103 hasConceptScore W4287165103C111472728 @default.
- W4287165103 hasConceptScore W4287165103C11413529 @default.
- W4287165103 hasConceptScore W4287165103C114614502 @default.
- W4287165103 hasConceptScore W4287165103C117898588 @default.
- W4287165103 hasConceptScore W4287165103C121332964 @default.
- W4287165103 hasConceptScore W4287165103C134306372 @default.
- W4287165103 hasConceptScore W4287165103C138885662 @default.
- W4287165103 hasConceptScore W4287165103C158622935 @default.
- W4287165103 hasConceptScore W4287165103C159694833 @default.
- W4287165103 hasConceptScore W4287165103C162324750 @default.
- W4287165103 hasConceptScore W4287165103C177148314 @default.
- W4287165103 hasConceptScore W4287165103C182306322 @default.
- W4287165103 hasConceptScore W4287165103C194777461 @default.
- W4287165103 hasConceptScore W4287165103C199360897 @default.
- W4287165103 hasConceptScore W4287165103C24890656 @default.
- W4287165103 hasConceptScore W4287165103C2775997480 @default.
- W4287165103 hasConceptScore W4287165103C2777303404 @default.
- W4287165103 hasConceptScore W4287165103C2778112365 @default.
- W4287165103 hasConceptScore W4287165103C2780586882 @default.
- W4287165103 hasConceptScore W4287165103C28826006 @default.
- W4287165103 hasConceptScore W4287165103C33923547 @default.
- W4287165103 hasConceptScore W4287165103C41008148 @default.
- W4287165103 hasConceptScore W4287165103C50522688 @default.
- W4287165103 hasConceptScore W4287165103C54355233 @default.
- W4287165103 hasConceptScore W4287165103C62520636 @default.
- W4287165103 hasConceptScore W4287165103C85189116 @default.
- W4287165103 hasConceptScore W4287165103C86803240 @default.
- W4287165103 hasConceptScore W4287165103C90119067 @default.
- W4287165103 hasConceptScore W4287165103C93926214 @default.
- W4287165103 hasConceptScore W4287165103C97137487 @default.
- W4287165103 hasLocation W42871651031 @default.
- W4287165103 hasOpenAccess W4287165103 @default.
- W4287165103 hasPrimaryLocation W42871651031 @default.
- W4287165103 hasRelatedWork W1975544700 @default.
- W4287165103 hasRelatedWork W2020715639 @default.
- W4287165103 hasRelatedWork W2049282606 @default.
- W4287165103 hasRelatedWork W2066640127 @default.
- W4287165103 hasRelatedWork W2085382584 @default.
- W4287165103 hasRelatedWork W2379238906 @default.
- W4287165103 hasRelatedWork W2953076669 @default.
- W4287165103 hasRelatedWork W2955846225 @default.
- W4287165103 hasRelatedWork W3208935936 @default.
- W4287165103 hasRelatedWork W2575171811 @default.
- W4287165103 isParatext "false" @default.
- W4287165103 isRetracted "false" @default.
- W4287165103 workType "article" @default.