Comparison results for splitting iterations for solving multi-linear systems
It is known that the spectral radius of the iterative tensor associated with a stationary splitting method (like the Jacobi or Gauss-Seidel methods) can be seen as an approximate convergence rate for solving multi-linear systems. The paper first gives some spectral radius comparisons between different types of tensor splittings. Then, it proposes a particular preconditioned tensor splitting method with a tensor analogue of a bidiagonal preconditioner. The corresponding spectral radius is analyzed in dependence of the chosen entries of this preconditioner and compared with the situation without preconditioner. Numerical examples are given to demonstrate the efficiency of the preconditioned methods applied in both a Gauss-Seidel and an SOR-type of setting.
scientific article; zbMATH DE number 6933820
scientific article