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Evaluation schemes in the ring of quaternionic polynomials. (English) Zbl 06858769
Summary: 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.

MSC:
65Y20 Complexity and performance of numerical algorithms
11R52 Quaternion and other division algebras: arithmetic, zeta functions
12Y05 Computational aspects of field theory and polynomials (MSC2010)
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