Extrapolated PSS Iterative Method for Sub-positive Definite Quaternion Equations

In this paper, we introduce a new splitting, called positive-definite and skew-self-conjugate splitting (PSS), and then establish a class of PSS methods similar to the Hermitian and skew-Hermitian splitting (HSS) method for iteratively solving the sub-positive definite matrix equation, and equivalently transform it iterative format on the basis of the PSS iteration method, heuristically establishes the extrapolated PSS iteration method. Theoretical analyses show that the PSS iteration method unconditionally converges to the exact solution of the equation. Using equivalent relationship between both PSS and extrapolated PSS iterations, the extrapolated PSS iteration method converges under certain conditions. Moreover, we minimize the upper bound of the spectral radius of iteration matrix. Finally, Numerical examples illustrating the effectiveness of both PSS and extrapolated PSS iterations are presented.