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On the convergence theory of double K-weak splittings of type II
Vaibhav Shekhar1, Nachiketa Mishra2, Debasisha Mishra1
1Department of Mathematics, National Institute of Technology, Great Eastern Rd, Raipur, Chhattisgarh, 492001 India.
Abstract:
Recently, Wang (2017) has introduced the K-nonnegative double splitting using the notion of matrices that leave a cone K ⊆ ℝ invariant and studied its convergence theory by generalizing the corresponding results for the nonnegative double splitting by Song and Song (2011). However, the convergence theory for K-weak regular and K-nonnegative double splittings of type II is not yet studied. In this article, we first introduce this class of splittings and then discuss the convergence theory for these sub-classes of matrices. We then obtain the comparison results for two double splittings of a K-monotone matrix. Most of these results are completely new even for . The convergence behavior is discussed by performing numerical experiments for different matrices derived from the discretized Poisson equation.
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