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9.2 Parallelism and Data Locality in Preconditioned CG     continued...

We consider another variant of CG, in which we may overlap all communication time with useful computations. This is just a reorganized version of the original CG scheme, and is therefore precisely as stable. The key trick is to delay the updating of the solution vector. Another advantage over the previous scheme is that no additional operations are required. We will assume that the preconditioner K can be written as . Furthermore, L has a block structure, corresponding to the grid blocks, so that any communication can again be overlapped with computation.