Multigrid Methods for General Block Toeplitz Matrices

In this paper we discuss multigrid methods for symmetric positive definite Block Toeplitz matrices. Our Block Toeplitz systems are general in the sense that the individual blocks are not necessarily Toeplitz. We investigate how transfer operators for prolongation and restriction have to be chosen such that our multigrid algorithms converge quickly. We will point out why these transfer operators can be understood as block matrices as well. We explain how our new algorithms can also be combined efficiently with the use of a natural coarse grid operator. Furthermore, we see that our block approach also comes out to be helpful for special Toeplitz matrices. Plenty of numerical experiments confirm that our multigrid solvers lead to optimal order convergence.     «

In this paper we discuss multigrid methods for symmetric positive definite Block Toeplitz matrices. Our Block Toeplitz systems are general in the sense that the individual blocks are not necessarily Toeplitz. We investigate how transfer operators for prolongation and restriction have to be chosen such that our multigrid algorithms converge quickly. We will point out why these transfer operators can be understood as block matrices as well. We explain how our new algorithms can also be combined ef...     »