Abstract
In this paper we focus on the study of monic polynomials whose coefficients are quaternions located on the left-hand side of the powers, by addressing three fundamental polynomial problems: factor, evaluate and deflate. An algorithm combining a deflaction procedure with a Weierstrass-like quaternionic method is presented. Several examples illustrate the proposed approach.
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Notes
- 1.
A polynomial P of degree n has only simple roots if it has n distinct isolated roots.
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Acknowledgments
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. (2022). A Modified Quaternionic Weierstrass Method. In: Gervasi, O., Murgante, B., Misra, S., Rocha, A.M.A.C., Garau, C. (eds) Computational Science and Its Applications – ICCSA 2022 Workshops. ICCSA 2022. Lecture Notes in Computer Science, vol 13377. Springer, Cham. https://doi.org/10.1007/978-3-031-10536-4_27
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