Abstract
Recently, Tian et al. [Computers and Mathematics with Applications, 75(2018): 2710-2722] came up with the inner-outer iterative method to solve the linear equation Ax=b and studied the corresponding convergence of the method. In this paper, we improve the main results of the inner-outer method and get weaker convergence results. Moreover, the parameters can be adjusted suitably so that the convergence property of the method can be substantially improved.
Highlights
When it comes to solving the large sparse linear system Ax b, (1)where A ∈ RN×N is a square nonsingular matrix and x, b ∈ RN, an iterative method is commonly used
Bai [2,3,4,5,6,7,8,9] did a mountain of great work and constructed the parallel nonlinear AOR method about matrix multisplitting, the parallel chaotic multisplitting method, the two-stage multisplitting method under suitable constraints about two-stage multisplitting, some new hybrid algebraic multilevel preconditioning algorithms, nonstationary multisplitting iterative algorithms, and the nonstationary multisplitting two-stage iterative algorithms
En, the inner-outer iterative algorithm is given in Algorithm 1
Summary
Where A ∈ RN×N is a square nonsingular matrix and x, b ∈ RN, an iterative method is commonly used. Bai [2,3,4,5,6,7,8,9] did a mountain of great work and constructed the parallel nonlinear AOR method about matrix multisplitting, the parallel chaotic multisplitting method, the two-stage multisplitting method under suitable constraints about two-stage multisplitting, some new hybrid algebraic multilevel preconditioning algorithms, nonstationary multisplitting iterative algorithms, and the nonstationary multisplitting two-stage iterative algorithms. Tian et al [22] studied the inner-outer iterative method for the linear equation Ax b and deduced the corresponding convergence of the inner-outer algorithm. Compared with those earlier studies, our findings of convergence results are more applicable. Our new convergent domain of the parameter α is wider than that in [22]. erefore, the convergence property of the method can be substantially improved due to the suitable adjustability of the parameters we adopted
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