BIT Numerical Mathematics

, Volume 58, Issue 1, pp 51–72 | Cite as

Evaluation schemes in the ring of quaternionic polynomials

  • M. Irene FalcãoEmail author
  • Fernando Miranda
  • Ricardo Severino
  • M. Joana Soares


In this paper we focus on computational aspects associated with polynomial problems in the ring of one-sided quaternionic polynomials. The complexity and error bounds of quaternion arithmetic are considered and several evaluation schemes are analyzed from their complexity point of view. The numerical stability of generalized Horner’s and Goertzel’s algorithms to evaluate polynomials with quaternion floating-point coefficients is addressed. Numerical tests illustrate the behavior of the algorithms from the point of view of performance and accuracy.


Quaternions Polynomial evaluation Error analysis 

Mathematics Subject Classification

65Y20 11R52 12Y05 



The authors would like to thank an anonymous referee for the valuable and constructive suggestions.


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.CMAT - Centre of Mathematics and DMA - Department of Mathematics and ApplicationsUniversity of MinhoBragaPortugal
  2. 2.DMA - Department of Mathematics and ApplicationsUniversity of MinhoBragaPortugal
  3. 3.NIPE - Economics Politics Research Unit and DMA - Department of Mathematics and ApplicationsUniversity of MinhoBragaPortugal

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