Weierstrass method for quaternionic polynomial root-finding
| Autor: | M. Irene Falcão, Fernando Miranda, M. Joana Soares, Ricardo Severino |
|---|---|
| Přispěvatelé: | Universidade do Minho |
| Rok vydání: | 2017 |
| Předmět: |
65H04
12D10 11R52 12Y05 Science & Technology Generalization General Mathematics Numerical analysis 010102 general mathematics General Engineering Weierstrass algorithm 010103 numerical & computational mathematics Numerical Analysis (math.NA) 01 natural sciences Algebra Polynomial root finding Convergence (routing) Quaternionic polynomials FOS: Mathematics Mathematics - Numerical Analysis 0101 mathematics Quaternion Root-finding methods Complex number Mathematics |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| DOI: | 10.48550/arxiv.1702.04935 |
| Popis: | Quaternions, introduced by Hamilton in 1843 as a generalization of complex numbers, have found, in more recent years, a wealth of applications in a number of different areas that motivated the design of efficient methods for numerically approximating the zeros of quaternionic polynomials. In fact, one can find in the literature recent contributions to this subject based on the use of complex techniques, but numerical methods relying on quaternion arithmetic remain scarce. In this paper, we propose a Weierstrass-like method for finding simultaneously all the zeros of unilateral quaternionic polynomials. The convergence analysis and several numerical examples illustrating the performance of the method are also presented. Research at CMAT was financed by Portuguese Funds through FCT, within the Project UID/MAT/00013/2013. Research at NIPE was carried out within the funding with COMPETE reference number POCI-01-0145-FEDER-006683 (UID/ECO/03182/2013), with the FCT/MEC’s (Funda¸c˜ao para a Ciˆencia e a Tecnologia, I.P.) financial support through national funding and by the ERDF through the Operational Programme on “Competitiveness and Internationalization - COMPETE 2020” under the PT2020 Partnership Agreement. info:eu-repo/semantics/publishedVersion |
| Databáze: | OpenAIRE |
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