An Iterative Method to Compute the Dominant Zero of a Quaternionic Unilateral Polynomial

作者：Serodio Rogerio^*; Ferreira Jose Augusto; Vitoria Jose

来源：Advances in Applied Clifford Algebras, 2018, 28(2): UNSP 45.

DOI：10.1007/s00006-018-0866-7

• Division algebra
• Polynomials
• Zeros of polynomials
• Quaternion

The aim of this paper is to propose an iterative method to compute the dominant zero of a quaternionic unilateral polynomial. We prove that the method is convergent in the sense that it generates a sequence of quaternions that converges to the dominant zero of the polynomial. The idea subjacent to this method is the well known Sebastiao e Silva's method, proposed in "Sur une methode d'approximation semblable a celle de Graffe", Portugaliae Mathematica, 1941, to approximate the dominant zero of complex polynomials.

• 出版日期2018-5