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Matrix splitting and its convergence theorems are useful tools for finding solution of linear system of equations, iteratively. In this article, we introduce a few matrix splittings arising from index-proper splittings. Then their convergence results and their applications to multisplitting theory are studied.

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Matrix splittings are useful in finding a solution of linear systems of equations, iteratively. In this note, we present some more convergence and comparison results for recently introduced matrix splittings called index-proper regular and index-proper weak regular splittings. We then apply to theory of double index-proper splittings.