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Classifying zeros of
two-sided quaternionic polynomials and computing zeros of
two-sided polynomials with complex coefficients
Feng Lianggui and Zhao Kaiming |
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Vol. 262 (2013), No. 2, 317–337
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Abstract |
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We improve the method of Janovská and Opfer for computing the zeros on the surface of a given sphere for a quaternionic two-sided polynomial. We classify the zeros of quaternionic two-sided polynomials into three types —isolated, spherical and circular—and characterize each type. We provide a method to find all quaternion zeros for two-sided polynomials with complex coefficients. We also establish standard formulae for roots of a quadratic two-sided polynomial with complex coefficients, which yields a simpler and more efficient algorithm to produce all zeros in the quadratic case. |
Keywords
quaternion, root, two-sided polynomial
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Mathematical Subject Classification 2010
Primary: 11R52, 12Y05, 12E15
Secondary: 15A03
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Milestones
Received: 1 February 2012
Revised: 8 October 2012
Accepted: 13 October 2012
Published: 16 April 2013
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Authors |
| Feng Lianggui | |
| Department of Mathematics and
Systems Science National University of Defense Technology Changsha, 410073 China |
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| Zhao Kaiming | |
| Department of Mathematics Wilfrid Laurier University Waterloo, ON N2L 3C5 Canada |
College of Mathematics and
Information Science Hebei Normal Teachers University Shijiazhuang Hebei, 050016 China |
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