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.
"Extensions of theory of regular and weak regular splittings to singular matrices." Adv. Oper. Theory 3 (2) 411 - 422, Spring 2018. https://doi.org/10.15352/AOT.1706-1188