In order to solve a linear system Ax=b, certain elementary row operations are performed on A before applying the Gauss-Seidel or Jacobi iterative methods. It is shown that when A is a nonsingular M-matrix or a singular tridiagonal M-matrix, the modified method yields considerable improvement in the rate of convergence for the iterative method. It is also shown that in some cases this method is superior to certain other modified iterative methods. The performance of this modified method on some matrices other than M-matrices is also investigated. © 1991.
Gunawardena, A. D., Jain, S. K., & Snyder, L. (1991). Modified iterative methods for consistent linear systems. Linear Algebra and Its Applications, 154–156(C), 123–143. https://doi.org/10.1016/0024-3795(91)90376-8