Convergence of the cyclical relaxation method for linear inequalities

@article{Mandel1984ConvergenceOT,
  title={Convergence of the cyclical relaxation method for linear inequalities},
  author={Jan Mandel},
  journal={Math. Program.},
  year={1984},
  volume={30},
  pages={218-228}
}
The relaxation method for linear inequalities is studied and new bounds on convergence obtained. An asymptotically tight estimate is given for the case when the inequalities are processed in a cyclical order. An improvement of the estimate by an order of magnitude takes place if strong underrelaxation is used. Bounds on convergence usually involve the so-called condition number of a system of linear inequalities, which we estimate in terms of their coefficient matrix.