Multi-iterative methods
The author considers a general class of iterative methods for solving systems of linear algebraic equations with a positive definite system matrix. These methods use two or more different iterative techniques, where each of them reduces the error by a constant factor in a different subspace of \(\mathbb{R}^ n\). At first multigrid methods as examples of such methods are analyzed. Using a prolongation operator with a special ``antidiagonal'' structure multigrid methods for Toeplitz and block-Toeplitz matrices are proposed. Finally, it is shown by numerical results that the convergence factor of the discussed algorithms is independent of the mesh size parameter.
scientific article; zbMATH DE number 474539