Zeros and singular points for one-sided coquaternionic polynomials with an extension to other \(R^4\) algebras

zbMath1307.65060MaRDI QIDQ2510841

Gerhard Opfer, Drahoslava Janovská

Publication date: 4 August 2014

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://www.emis.de/journals/ETNA/volumes/2011-2020/vol41/abstract_vol41_pp133-158.html

zbMATH Keywords

``weak fundamental theorem of algebra for coquaternionscompanion polynomial for coquaternionic polynomialsconectarinescotangerines)cotessarinesexact Jacobi matrix for coquaternionic polynomialsnectarinesNewton method for coquaternionic polynomialssingular points for coquaternionic polynomialstangerineszeros of coquaternionic polynomialszeros of polynomials in other \(R^4\) algebras (tessarineszeros of polynomials in split quaternions

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Quaternion and other division algebras: arithmetic, zeta functions (11R52) Skew fields, division rings (12E15) Numerical computation of roots of polynomial equations (65H04)

Related Items (8)

Matrices over nondivision algebras without eigenvalues ⋮ Niven's algorithm applied to the roots of the companion polynomial over \(\mathbb {R}^4\) algebras ⋮ Algebraic techniques for eigenvalues and eigenvectors of a nectarine matrix in nectarine algebra ⋮ Newton’s Approach to General Algebraic Equations over Clifford Algebras ⋮ The algebra of slice functions ⋮ The number of zeros of unilateral polynomials over coquaternions revisited ⋮ The relation between the companion matrix and the companion polynomial in \(\mathbb {R}^4\) algebras ⋮ The Jacobi matrix for functions in noncommutative algebras

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