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

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. 379

• Type: Journal
• Year: 2010
• Where: SIAMNUM
• Authors: Drahoslava Janovská, Gerhard Opfer
• Keywords: Polynomials, Quaternionic Polynomials, SIAMNUM 2010, Spherical Zeros