Weierstrass method for quaternionic polynomial root‐finding. (10th November 2017)

• Record Type: Journal Article
• Authors: Falcão, M. Irene; Miranda, Fernando; Severino, Ricardo; Soares, M. Joana
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 1(2018)
• Page Start: 423
• Page End: 437
• Publication Date: 2017-11-10
• Subjects: quaternionic polynomials -- root‐finding methods -- Weierstrass algorithm; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4623
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.