A Two-step Quaternionic Root-finding Method

• Author(s): Falcão, M. I. ; Miranda, Fernando ; Severino, Ricardo ; Soares, M. J.
• Date: 2023
• Persistent ID: https://hdl.handle.net/1822/86298
• Origin: RepositóriUM - Universidade do Minho
• Subject(s): Quaternions; Weierstrass method; Zeros
• Document Type: Conference paper
• Language: English
• Contributor(s): Universidade do Minho

Description

In this paper we present a new method for determining simultaneously all the simple roots of a quaternionic polynomial. The proposed algorithm is a two-step iterative Weierstrass-like method and has cubic order of convergence. We also illustrate a variation of the method which combines the new scheme with a recently proposed deflation procedure for the case of polynomials with spherical roots.