Weierstrass method for quaternionic polynomial root-finding
It addresses the need for efficient numerical methods in quaternion arithmetic for root-finding, which is important for applications in areas like robotics and computer graphics.
The paper proposes a Weierstrass-like method for simultaneously finding all zeros of unilateral quaternionic polynomials, with convergence analysis and numerical examples demonstrating its performance.
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 which 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 {\sl all} the zeros of unilateral quaternionic polynomials. The convergence analysis and several numerical examples illustrating the performance of the method are also presented.