Evaluation schemes in the ring of quaternionic polynomials
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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.
KeywordsQuaternions Polynomial evaluation Error analysis
Mathematics Subject Classification65Y20 11R52 12Y05
The authors would like to thank an anonymous referee for the valuable and constructive suggestions.
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