A note on defect correction processes with an approximate inverse of deficient rank

AbstractIn view of the analysis of multiple grid methods, in this note we consider defect correction processes of deficient rank. Both for the error and for the residual, the convergence of the defect iterative process is studied in terms of the range and the kernel of the approximate inverse. Since the coarse grid correction in the multiple grid algorithm can be seen as a step in such an iterative process, the present study can be used in the convergence analysis of these algorithms. It shows that pre-relaxation is advantageous for reducing the error, whereas post-relaxation is better for reducing the residual