Algorithms for quaternion polynomial root-finding

DOI10.1016/j.jco.2013.03.001zbMath1326.65060OpenAlexW1993304545MaRDI QIDQ2434926

Bahman Kalantari

Publication date: 3 February 2014

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2013.03.001

zbMATH Keywords

Newton's methodrecurrence relationquaternionsfundamental theorem of algebrapolynomial rootspolynomiography

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Computational aspects of associative rings (general theory) (16Z05) Numerical computation of roots of polynomial equations (65H04)

Related Items

Bounds for eigenvalues of matrix polynomials over quaternion division algebra ⋮ Newton method in the context of quaternion analysis ⋮ General theory of the higher-order linear quaternion q-difference equations through the quaternion determinant algorithm and the characteristic polynomial ⋮ An iterative method to compute the dominant zero of a quaternionic unilateral polynomial ⋮ A non-commutative cryptosystem based on quaternion algebras ⋮ Factorization and root-finding for polynomials over division quaternion algebras ⋮ Solution of a quadratic quaternion equation with mixed coefficients ⋮ Niven's algorithm applied to the roots of the companion polynomial over \(\mathbb {R}^4\) algebras ⋮ Complex Roots of Quaternion Polynomials ⋮ Perturbation analysis of matrices over a quaternion division algebra ⋮ General theory of the higher-order quaternion linear difference equations via the complex adjoint matrix and the quaternion characteristic polynomial ⋮ Factoring skew polynomials over Hamilton's quaternion algebra and the complex numbers ⋮ Basis-free solution to general linear quaternionic equation ⋮ Roots of quaternion polynomials: theory and computation ⋮ Global behaviour of quaternion Riccati rational difference equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Polynomial root-finding methods whose basins of attraction approximate Voronoi diagram
• Computing quaternionic roots by Newton's method
• Numerical methods for roots of polynomials. Part I
• Polynomials and Vandermonde matrices over the field of quaternions
• A new method for roots of monic quaternionic quadratic polynomial
• Sur les équations polynomiales dans les quaternions
• A basic family of iteration functions for polynomial root finding and its characterizations
• Quadratic formulas for quaternions
• De Moivre's formula for quaternions
• The double determinant of Vandermonde's type over quaternion field
• A three-stage variable-shift iteration for polynomial zeros and its relation to generalized Rayleigh iteration
• An efficient algorithm for the complex roots problem
• On efficient computation and asymptotic sharpness of Kalantari’s bounds for zeros of polynomials
• Zeros of unilateral quaternionic polynomials
• Polynomials with Coefficients from a Division Ring
• Solving a Polynomial Equation: Some History and Recent Progress
• Iteration of Quaternion Functions
• An infinite family of bounds on zeros of analytic functions and relationship to Smale’s bound
• On the Structure of the Set of Zeros of Quaternionic Polynomials
• On the iteration of quaternionic moebius transformations
• On the Zeros of Polynomials over Division Rings
• Dynamics in One Complex Variable. (AM-160)
• Equations in Quaternions
• The Roots of a Quaternion
• The Roots of a Quaternion
• The “fundamental theorem of algebra” for quaternions
• Generalization of Taylor's theorem and Newton's method via a new family of determinantal interpolation formulas and its applications
• On left eigenvalues of a quaternionic matrix
• Zeros of quaternion polynomials
• Computing the zeros of quaternion polynomials.
• Quaternions and matrices of quaternions