A new method of finding all Roots of simple quaternionic polynomials

Details A new method of finding all Roots of simple quaternionic polynomials A new method of finding all Roots of simple quaternionic polynomials

2011-09-12

arxiv.org/abs/1109.2503v2

Mathematics

Rings and Algebras

19 pages

Scientific paper

In this paper, we provide a new method to find all zeros of polynomials with quaternionic coefficients located on only one side of the powers of the variable (these polynomials are called simple polynomials). This method is much more efficient and much simpler than the known one in [D. Janovska and G. Opfer, A note on the computation of all zeros of simple quaternionic polynomials, SIAM J. Numer. Anal., 48(1)(2010), pp. 244-256]. We recover several known results, and deduce several interesting consequences concerning solving equations with all real coefficients or complex coefficients which do not seem to be deduced easily from the results in [D. Janovska and G. Opfer, A note on the computation of all zeros of simple quaternionic polynomials, SIAM J. Numer. Anal., 48(1)(2010), pp. 244-256]. We also give a necessary and sufficient condition for a simple quaternionic polynomials to have finitely many solutions (only isolated solutions).

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