Abstract
In this paper we present a new method for determining simultaneously all the simple roots of a quaternionic polynomial. The proposed algorithm is a two-step iterative Weierstrass-like method and has cubic order of convergence. We also illustrate a variation of the method which combines the new scheme with a recently proposed deflation procedure for the case of polynomials with spherical roots.
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Notes
- 1.
The zeros are all simple if they are all distinct and isolated.
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Acknowledgment
Research at CMAT was partially financed by Portuguese funds through FCT - Fundação para a Ciência e a Tecnologia, within the Projects UIDB/00013/2020 and UIDP/00013/2020. Research at NIPE has been financed by FCT, within the Project UIDB/03182/2020.
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Falcão, M.I., Miranda, F., Severino, R., Soares, M.J. (2023). A Two-Step Quaternionic Root-Finding Method. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2023 Workshops. ICCSA 2023. Lecture Notes in Computer Science, vol 14104. Springer, Cham. https://doi.org/10.1007/978-3-031-37105-9_47
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