Weierstrass method for quaternionic polynomial root-finding

• Autor(a) principal: Falcão, M. I.
• Data de Publicação: 2018
• Outros Autores: Miranda, Fernando, Severino, Ricardo, Soares, M. J.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/1822/51931
• topic: Quaternionic polynomials; Root-finding methods; Weierstrass algorithm; Science & Technology

Quaternions, introduced by Hamilton in 1843 as a generalization of complex numbers, have found, in more recent years, a wealth of applications in a number of different areas that motivated the design of efficient methods for numerically approximating the zeros of quaternionic polynomials. In fact, one can find in the literature recent contributions to this subject based on the use of complex techniques, but numerical methods relying on quaternion arithmetic remain scarce. In this paper, we propose a Weierstrass-like method for finding simultaneously all the zeros of unilateral quaternionic polynomials. The convergence analysis and several numerical examples illustrating the performance of the method are also presented.