A note on defect correction processes with an approximate inverse of deficient rank
Copyright policy )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.
post-relaxation, Iterative numerical methods for linear systems, convergence, Applied Mathematics, pre-relaxation, Numerical solution of discretized equations for boundary value problems involving PDEs, multiple grid methods, defect correction processes of deficient rank, Banach spaces, Computational Mathematics, Boundary value problems for second-order elliptic equations, approximate inverse, Numerical solutions to equations with linear operators, Equations and inequalities involving linear operators, with vector unknowns
post-relaxation, Iterative numerical methods for linear systems, convergence, Applied Mathematics, pre-relaxation, Numerical solution of discretized equations for boundary value problems involving PDEs, multiple grid methods, defect correction processes of deficient rank, Banach spaces, Computational Mathematics, Boundary value problems for second-order elliptic equations, approximate inverse, Numerical solutions to equations with linear operators, Equations and inequalities involving linear operators, with vector unknowns
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