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Roots Of Quaternionic Polynomials And Automorphisms Of Roots, Olalekan Ogunmefun
Roots Of Quaternionic Polynomials And Automorphisms Of Roots, Olalekan Ogunmefun
Electronic Theses and Dissertations
The quaternions are an extension of the complex numbers which were first described by Sir William Rowan Hamilton in 1843. In his description, he gave the equation of the multiplication of the imaginary component similar to that of complex numbers. Many mathematicians have studied the zeros of quaternionic polynomials. Prominent of these, Ivan Niven pioneered a root-finding algorithm in 1941, Gentili and Struppa proved the Fundamental Theorem of Algebra (FTA) for quaternions in 2007. This thesis finds the zeros of quaternionic polynomials using the Fundamental Theorem of Algebra. There are isolated zeros and spheres of zeros. In this thesis, we …
Enestr¨Om-Kakeya Type Results For Complex And Quaternionic Polynomials, Matthew Gladin
Enestr¨Om-Kakeya Type Results For Complex And Quaternionic Polynomials, Matthew Gladin
Electronic Theses and Dissertations
The well known Eneström-Kakeya Theorem states that: for P(z)=∑i=0n ai zi, a polynomial of degree n with real coefficients satisfying 0 ≤ a0 ≤ a1 ≤ ⋯≤ an, all zeros of P(z) lie in |z|≤1 in the complex plane. In this thesis, we will find inner and outer bounds in which the zeros of complex and quaternionic polynomials lie. We will do this by imposing restrictions on the real and imaginary parts, and on the moduli, of the complex and quaternionic coefficients. We also apply similar restrictions on complex polynomials with …