Complex Roots of Quaternion Polynomials

Πετρούλα Δόσπρα, Dimitrios Poulakis

Type: Book-Chapter

Publication Date: 2017-01-01

Citations: 0

DOI: https://doi.org/10.1007/978-3-319-56932-1_5

Abstract

In this paper, using hybrid Bézout matrices, we give necessary and sufficient conditions, for a quaternion polynomial to have a complex root, a spherical root, and a complex isolated root. These conditions can be easily checked since these matrices are implemented in the computational system MAPLE. Moreover, we compute upper bounds for the norm of the roots of a quaternion polynomial.

Locations

Springer proceedings in mathematics & statistics - View
arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Complex Roots of Quaternion Polynomials	2015	Πετρούλα Δόσπρα Dimitrios Poulakis
+	Complex Roots of Quaternion Polynomials	2015	Πετρούλα Δόσπρα Dimitrios Poulakis
+	Pure Imaginary Roots of Quaternion Standard Polynomials	2011	Adam Chapman
+	Pure Imaginary Roots of Quaternion Standard Polynomials	2011	Adam Chapman
+ PDF Chat	Classifying zeros of two-sided quaternionic polynomials and computing zeros of two-sided polynomials with complex coefficients	2013	Lianggui Feng Kaiming Zhao
+	Algorithms for quaternion polynomial root-finding	2013	Bahman Kalantari
+	Roots of Quaternion Standard Polynomials	2011	Adam Chapman
+	Roots of quaternion polynomials: Theory and computation	2019	Takis Sakkalis Kwang Hee Ko Galam Song
+	Characteristic roots of quaternion matrices	1954	Olga Taussky
+	The roots of a split quaternion	2008	Mustafa Özdemir
+	Resultants of Quaternion Polynomials	2018	Xiangui Zhao Yang Zhang
+	Complex Numbers	2010	Ron Goldman
+	Cubic formulas for computing the zeros of certain quaternionic polynomial	2017	Mingsheng Liu Yan Tang
+	Números complexos, quatérnions e rotações	2012	Michel Valmor dos Santos
+	Some Properties of Quaternion Algebra over the Sets of Real and Complex Numbers	2023	Țugui Andreea-Elena
+ PDF Chat	New insight into quaternions and their matrices	2023	Gülsüm Yeliz Şentürk Nurten Gürses Sali̇m Yüce
+ PDF Chat	Computational Aspects of Quaternionic Polynomials	2018	M. I. Falcão Fernando Miranda Ricardo Severino Maria Joana Soares
+	The Roots of a Quaternion	1942	Louis Brand
+	The Roots of a Quaternion	1942	Ivan Niven
+	Scalar–vector algorithm for the roots of quadratic quaternion polynomials, and the characterization of quintic rational rotation-minimizing frame curves	2013	Rida T. Farouki Πετρούλα Δόσπρα Takis Sakkalis

Works That Cite This (0)

Action	Title	Year	Authors

Works Cited by This (29)

Action	Title	Year	Authors
+	An inequality on the greates roots of a polynomial.	1991	Max Mignotte
+	The fundamental theorem of algebra	1998	Benjamin Fine Gerhard Rosenberger
+ PDF Chat	Zeros of regular functions and polynomials of a quaternionic variable	2008	Graziano Gentili Caterina Stoppato
+ PDF Chat	A Note on the Computation of All Zeros of Simple Quaternionic Polynomials	2010	Drahoslava Janovská Gerhard Opfer
+	The fundamental theorem of algebra for Hamilton and Cayley numbers	2007	Graziano Gentili Daniele C. Struppa Fabio Vlacci
+	Computing the zeros of quaternion polynomials	2001	Rogério Serôdio E. Pereira José Vitória
+	Algorithms for quaternion polynomial root-finding	2013	Bahman Kalantari
+	Generalized Resultant Theorem	1978	A.I.G. Vardulakis P. N. R. STOYLE
+	Zeros of quaternion polynomials	2001	Rogério Serôdio Lok-shun Siu
+	On roots of quaternion polynomials	2009	N. Topuridze