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An iterative method to compute the dominant zero of a quaternionic unilateral polynomial. (English) Zbl 1397.65070
Summary: 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 Sebastião e Silva’s method, proposed in [J. Sebastião e Silva, Port. Math. 2, 271–279 (1941; Zbl 0026.05303)] to approximate the dominant zero of complex polynomials.
##### MSC:
 65H04 Numerical computation of roots of polynomial equations 12E15 Skew fields, division rings
##### Keywords:
division algebra; polynomials; zeros of polynomials; quaternion
Full Text:
##### References:
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