On the Higher Order Sylvester quaternion equation alpha q(n)

被引：0

作者：

Boukas, Andreas ^{[1
]}

Fellouris, Anargyros ^{[2
]}

机构：

[1] Univ Roma Tor Vergata, Ctr Vito Volterra, Via Columbia 2, I-00133 Rome, Italy

[2] Natl Tech Univ Athens, Fac Appl Sci, Dept Math, Athens 15780, Greece

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE | 2015年 / 10卷 / 02期

关键词：

Sylvester equation; quaternion; quaternion equation; n-th root of a quaternion; Newton-Raphson method; non-linear systems of equations;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the existence of quaternion solutions q of the Higher Order Sylvester equation aq(n) + q(n)b = c where n = 2, 3,... and a, b, c are quaternions. In the cases when solutions exist an explicit formula for them is provided using both the Hamilton and matrix representation of quaternions. The recursive solution of polynomial quaternion equations and in particular of the Higher Order Sylvester equation using the Newton-Raphson scheme for non-linear systems of equations is also discussed.

引用

页码：139 / 156

页数：18

共 13 条

[1] Cheney W., 1991, NUMERICAL ANAL MATH
[2] De Leo S., 2006, ELECTRON J LINEAR AL, V15
[3] The Quaternionic Equation ax+xb = c
Helmstetter, Jacques
[J]. ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2012, 22 (04) : 1055 - 1059
[4] Janovska D., 2008, MITT MATH GES HAMBUR, V27, P223
[5] Janovska D., 2007, ELECTRON T NUMER ANA, V26, P82102
[6] A NOTE ON THE COMPUTATION OF ALL ZEROS OF SIMPLE QUATERNIONIC POLYNOMIALS
Janovska, Drahoslava
Opfer, Gerhard
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2010, 48 (01) : 244 - 256
[7] Matiadou N. L., 2015, J MULTIDISCIPLINARY, V2, P334
[8] Linear Manifolds in Sets of Solutions of Quaternionic Polynomial Equations of Several Types
Mierzejewski, Dmytro
[J]. ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2011, 21 (02) : 417 - 428
[9] Morais J.P., 2014, REAL QUATERNIONIC CA
[10] Niven I., 2004, AM MATH MONTHLY, V49, P379

← 1 2 →