Semi-Iterative and Iterative Methods for Singular M -Matrices
George P. Barker, Shiyun Yang · SIAM Journal on Matrix Analysis and Applications · 1988
This paper provides a theoretical basis for establishing the convergence of semi-iterative and iterative techniques, especially Jacobi and Gauss–Seidel techniques, for computing nontrivial solutions of $Ax = 0$ where A is a singular M-matrix. These results do not assume A to be irreducible. The convergence question for iterative techniques continues to be studied extensively. The interest has been primarily in rearranging states on the rate of convergence. Here we begin the investigation of an alternate technique, namely a semi-iterative or averaging process, to attain convergence.