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For the coupled Lyapunov problem derived from continuous Markov jump systems, a new implicit single-step splitting(ISS) iterative algorithm is proposed based on the idea of single step split iteration. After that, the accelerated implicit single-step splitting(AISS) iterative method, which is an accelerated algorithm of ISS iterative method, is proposed by using the idea of two-step alternate iteration. In this paper, the relevant convergence proofs of ISS and AISS iteration methods are given. Then, the selection range of the parameters of ISS and AISS iteration methods and the selection method of optimal parameters are given. Finally, this paper demonstrates the feasibility and advantage of the novel methods through actual calculations.

Accelerated Implicit Single-Step Splitting Iteration Method for a Class of Coupled Lyapunov Equations