Convergence of H-double Splitting for H-matrices

Regularized iterative method for ill-posed linear systems based on matrix splitting

“…is less than one, i.e., ρ(W) < 1. More on the convergence of the scheme (7) concerning different types of splittings and its comparison analysis can be found in [22], [33], and [49]. In addition to these, Mishra [33] introduced the double proper nonnegative splitting which we renamed as the double proper weak splitting of type I and defined as follows.…”

Alternating Stationary Iterative Methods Based on Double Splittings

“…Such type of splitting leads to the iterative scheme x k+1 = P −1 Rx k − P −1 Sx k−1 + P −1 b, k > 0 for solving the non-singular linear system (1.1), when n = m. Shen and Huang [36] and Miao et al [26] studied the convergence and comparison of the above iterative scheme for monotone matrices (A ∈ R n×n is monotone [13] if and only if A −1 exists and A −1 ≥ 0). Moreover, several convergence and its comparison results exist in the literature for different types of double splittings (see [19], [20], [21], [25], [36], [37], [39], [41], [45]). In 2019, Li et al [23] proposed an alternating scheme using double splittings of a matrix to find an approximate solution of a real non-singular linear system of equations.…”