Residual Scaling Techniques in Multigrid , I : Equivalence Proof
نویسنده
چکیده
This paper addresses the residual scaling techniques (coarse-grid-correction optimization techniques) in multigrid methods. We survey recent developments in this area and prove the equivalence of the over-weighted residual technique and the over-correction technique. This leads to the proof of mathematical equivalence of the pre-scaling and post-scaling acceleration techniques. Two theorems have been proved to unify the concept of the residual scaling techniques. These theoretical results clear the way for developing eecient pre-scaling acceleration techniques for practical applications. Those practical pre-scaling acceleration techniques are discussed in a companion paper: Residual scaling techniques, II: practical applications.
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