Convergence and quotient convergence of iterative methods for solving singular linear equations with index one (Q1002268)

Let \(A\) be a matrix with index \(1\). The solution of a linear system \(Ax=b\) is possible in the quotient space \(\mathbb R^n/{N}(A)\) if \(N(A)\) denotes the kernel and \(b\) lies in the range of \(A\). Iterative solvers are considered modulo \({N}(A)\). Convergence to the solution of minimal norm is of special interest. The use of the group inverse admits a formal generalization of known convergence results for linear iterative methods.