BIT Numerical Mathematics

, Volume 52, Issue 2, pp 485–501 | Cite as

A new look at CMRH and its relation to GMRES



CMRH is a Krylov subspace method which uses the Hessenberg process to produce a basis of a Krylov method, and minimizes a quasiresidual. This method produces convergence curves which are very close to those of GMRES, but using fewer operations and storage. In this paper we present new analysis which explains why CMRH has this good convergence behavior. Numerical examples illustrate the new bounds.


Krylov subspace Arnoldi Hessenberg CMRH method GMRES 

Mathematics Subject Classification (2010)




We thank the referees for their comments and questions, which helped improve our presentation.

D.B. Szyld research supported in part by the U.S. Department of Energy under grant DE-FG02-05ER25672.


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© Springer Science + Business Media B.V. 2011

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Pures et AppliquéesUniversité du Littoral, Centre Universitaire de la Mi-VoixCalais CedexFrance
  2. 2.Department of MathematicsTemple University (038-16)PhiladelphiaUSA

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