A new look at CMRH and its relation to GMRES
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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.
KeywordsKrylov subspace Arnoldi Hessenberg CMRH method GMRES
Mathematics Subject Classification (2010)65F10
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.
- 6.Higham, N.J.: The matrix computation toolbox. Available online at http://www.ma.man.ac.uk/~higham/mctoolbox