Study On Row-Action Methods For Huge And Sparse Systems And Its Application To Two-dimensional Cutting-Stock Problems

This article mainly studies the row-action methods for huge and sparse systems. By using the concept of the row-action methods, the Jacobi iterative method, the Gauss-Seidel iterative method and the SOR iterative method for solving the system of linear equations are reanalyzed, a row-action method for solving the system of linear equations with positive semidefinite coefficient matrix (not necessarily symmetric) is derived, the convergence of these methods are proved by a unified approach. A new row-action method for solving the system of linear equations with positive semidefinite matrix (not necessarily symmetric) is considered, the numerical experiments show the method is very effective, however, its theoretical convergence is not proved yet. Based on summarizing the row-action methods for solving the system of linear inequalities and the convex feasibility problems, a row-action method for exactly solving the two-dimensional cutting-stock problems is presented, the availability of the method is shown by numerical examples.