Abstract
We present a new stationary iterative method, called Scale-Splitting (SCSP) method, and investigate its convergence properties. The SCSP method naturally results in a simple matrix splitting preconditioner, called SCSP-preconditioner, for the original linear system. Some numerical comparisons are presented between the SCSP-preconditioner and several available block preconditioners, such as PGSOR (Hezari et al. Numer. Linear Algebra Appl. 22, 761–776, 2015) and rotate block triangular preconditioners (Bai Sci. China Math. 56, 2523–2538, 2013), when they are applied to expedite the convergence rate of Krylov subspace iteration methods for solving the original complex system and its block real formulation, respectively. Numerical experiments show that the SCSP-preconditioner can compete with PGSOR-preconditioner and even more effective than the rotate block triangular preconditioners.
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Hezari, D., Salkuyeh, D.K. & Edalatpour, V. A new iterative method for solving a class of complex symmetric system of linear equations. Numer Algor 73, 927–955 (2016). https://doi.org/10.1007/s11075-016-0123-x
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DOI: https://doi.org/10.1007/s11075-016-0123-x