Block iterative methods for solving multi-linear systems

Abstract This work is concerned with the development of iterative methods for the solution of large multi-linear systems of equations that arise when discretizing partial differential equations as well as in other applications. Efficient iterative block methods of Jacobi, Gauss-Seidel, and SOR type that use a block partitioning of the coefficient tensor are proposed and their convergence properties are analyzed. Computed examples illustrate the usefulness of the proposed block methods.