Residual scaling techniques in multigrid, I: Equivalence proof

Jun Zhang

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


This paper addresses the residual scaling techniques (coarse-grid-correction optimization techniques) in multigrid methods. We surveyed recent developments in this area and prove the equivalence of the overweighted residual technique and the overcorrection technique. This leads to the proof of mathematical equivalence of the prescaling and postscaling acceleration techniques. Two theorems have been proved to unify the concept of the residual scaling techniques. These theoretical results clear the way for developing efficient prescaling acceleration techniques for practical applications. Those practical prescaling acceleration techniques are discussed in a companion paper: Residual scaling techniques, II: practical applications.

Original languageEnglish
Pages (from-to)283-303
Number of pages21
JournalApplied Mathematics and Computation
Issue number2-3
StatePublished - 1997

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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