Construction of Classes of Smoothers

In Section 3 a generic smoother R_k was introduced and was assumed to satisfy certain conditions. This section is devoted to the construction of two classes of smoothers which satisfy the relevant conditions. We will see in Section 10 that these classes of smoothers are constructed in such a way that the multigrid algorithms are easily implemented. These classes include the block Jacobi and Gauss–Seidel smoothers.