四元数亚正定系统混参分裂迭代方法

随着四元数的广泛应用,大型四元数结构矩阵方程的求解成为科学计算的重要课题。本文针对四元数亚正定系统AX=B,在NPSS迭代基础上通过引入双参数和松弛加速技术,构建出两种新的混参分裂迭代格式ANPSS和SANPSS,同时运用四元数矩阵特征值理论,证明了这两种迭代的收敛性,并给出相关参数的取值范围。此外我们采用四元数矩阵的复表示方法,在Matlab环境下实现该系统的数值求解。数值算例表明,多参数的灵活选取,显示出所提混参分裂迭代相比NPSS迭代具有更高的收敛效率。

Mixed parameter splitting iteration method for quaternion subpositive definite system

With the wide application of quaternions, the solution of large quaternion structured matrix equations has become an important topic in scientific computing. In this paper, for the quaternion positive definite system AX=B, two new mixed parameter splitting iterative schemes ANPSS and SANPSS are constructed by introducing two parameters and relaxation acceleration technology on the basis of NPSS iteration. At the same time, the convergence of these two iterations is proved by using the eigenvalue theory of quaternion matrix, and the range of relevant parameters is given. In addition, we use the complex representation method of quaternion matrix to realize the numerical solution of the system in Matlab environment. Numerical examples show that the flexible selection of multiple parameters shows that the proposed mixed parameter splitting iteration has higher convergence efficiency than NPSS iteration.