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 Ax = b and obtain the structure-preserving algorithms of Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems Ax = 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 Ax = b.

Automated summary

In this paper, the Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems Ax = b are studied and the structure-preserving algorithms of these methods are obtained. The convergence and computational cost of these iteration methods are discussed and numerical examples are given to demonstrate their efficiency. As an application, two kinds of structure-preserving iterative algorithms are applied to solve elliptic biquaternion linear systems Ax = b.