NDLI: A Note on the Computation of All Zeros of Simple Quaternionic Polynomials

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Janovsk, Drahoslava Opfer, Gerhard
Copyright Year	2010
Abstract	Polynomials with quaternionic coefficients located on only one side of the powers (we call them simple polynomials) may have two different types of zeros: isolated and spherical zeros. We will give a new characterization of the types of the zeros and, based on this characterization, we will present an algorithm for producing all zeros including their types without using an iteration process which requires convergence. The main tool is the representation of the powers of a quaternion as a real, linear combination of the quaternion and the number one (as introduced by Pogorui and Shapiro [Complex Var. and Elliptic Funct., 49 (2004), pp. 379389]) and the use of a real companion polynomial which already was introduced for the first time by Niven [Amer. Math. Monthly, 48 (1941), pp. 654661]. There are several examples.
Starting Page	244
Ending Page	256
Page Count	13
File Format	PDF
ISSN	00361429
DOI	10.1137/090748871
e-ISSN	10957170
Issue Number	1
Volume Number	48
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2010-04-02
Access Restriction	Subscribed
Subject Keyword	Skew fields, division rings Computational aspects of field theory and polynomials zeros of quaternionic polynomials Quaternion and other division algebras: arithmetic, zeta functions structure of zeros of quaternionic polynomials Single equations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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