(The) analysis of smoothers in multigrid algorithms for symmetric positive definite forms

Abstract

To analyze multigrid methods, we have some assumptions concerning the smoothing process. Smoothing operators considered are based on subspace decomposition and include point, line, and block Jacobi and Gauss-Seidel iteration as well as generalization. We shall show that assumptions are satisfied if the subspace decomposition satisfles two simple condition which are trivial to verify and verify assumptions by numerical experiment. We shall show that thses smoothers will be effective in multigrid algorithms.