# Prolongation/Restriction Operator in Multigrid

In Multigrid, using Poisson's equation, does the equality below always hold regardless of what type of boundary conditions you use? $$R= c\cdot I^T, \text{ for some constant }c$$ where $R$ and $I$ are the restriction and interpolation operator. Why or why not?

It's not a question whether the condition holds or not. You choose $R$ so that it's a multiple of $I^T$ because you want the condition to hold. You want the condition to hold because that's the only way you can ensure that the multigrid operator is symmetric and amenable to, say, being a preconditioner for CG.
• Ugh. My restriction operator wasn't handling inhomogeneous Dirichlet boundary conditions properly. So I wrote it separately...Meaning that as of now I have no $c$ s.t. the equality holds. Does this mean I'll have to reconfigure everything? – TheRealFakeNews Mar 19 '13 at 2:27