New structure-preserving algorithms of Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems

In this paper, we study the Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems A x = b and obtain the structure-preserving algorithms of Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems A x = b . The convergence and...

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Bibliographic Details
Published in:Numerical algorithms Vol. 95; no. 3; pp. 1309 - 1323
Main Authors: Ding, Wenxv, Liu, Zhihong, Li, Ying, Wei, Anli, Zhang, Mingcui
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2024
Springer Nature B.V
Subjects:
Algebra
Algorithms
Computer Science
Iterative algorithms
Iterative methods
Linear systems
Methods
Numeric Computing
Numerical Analysis
Numerical methods
Original Paper
Quaternions
Theory of Computation
Successive over-relaxation iteration
15A24
11R52
15B33
Quaternion linear systems
Gauss-Seidel iteration
Structure-preserving algorithm
15A09
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:In this paper, we study the Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems A x = b and obtain the structure-preserving algorithms of Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems A x = b . The convergence and computational cost of these iteration methods are discussed. Numerical examples are given to demonstrate the efficiency of structure-preserving algorithms of Gauss-Seidel iteration and successive over-relaxation iteration methods. As an application, we apply two kinds of structure-preserving iterative algorithms to solve elliptic biquaternion linear systems A x = b .
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-023-01609-7