On Thu, Feb 14, 2008 at 10:30 AM, Stephen R Ball
<Stephen.R.Ball at awe.co.uk> wrote:
>
>
> Hi
>
> Thanks for your suggestions. You have given a reference for CR
> (Conjugate Residuals) as:
>
> Methods of Conjugate Gradients for Solving Linear Systems, Magnus R.
> Hestenes and Eduard Stiefel, Journal of Research of the National Bureau
> of Standards Vol. 49, No. 6, December 1952 Research Paper 2379 pp.
> 409--436.
I get this:
The Conjugate Residual Method for Constrained Minimization Problems
David G. Luenberger
SIAM Journal on Numerical Analysis, Vol. 7, No. 3 (Sep., 1970), pp. 390-398
Barry, do you agree?
Matt
> However the PETSc user manual says this is the reference for CG
> (Conjugate Gradient). Can you clarify which is the case? If it is not
> for CR do you know of a reference for CR?
>
> If anyone can provide references for the Bi-CG, Chebychev, CR (Conjugate
> Residuals), QCG (Quadratic CG) and Richardson solvers that would be very
> much appreciated.
>
> Regards
>
> Stephen
>
>
>
>
> -----Original Message-----
> From: owner-petsc-users at mcs.anl.gov
> [mailto:owner-petsc-users at mcs.anl.gov] On Behalf Of Barry Smith
> Sent: 13 February 2008 20:41
> To: petsc-users at mcs.anl.gov
> Subject: EXTERNAL: Re: References for preconditioners and solver
> methods.
>
>
> I've started adding them to the manual pages. Here are the ones I
> have so far
>
> On Feb 13, 2008, at 6:12 AM, Stephen R Ball wrote:
>
> >
> > Hi
> >
> > I am writing a paper that references PETSc and the preconditioners and
> > linear solvers that it uses. I would like to include references for
> > these. I have searched and found references for quite a few but am
> > struggling to find references for the following solver methods:
> >
> > BICG
>
>
> >
> > CGNE
>
> This is just CG applied to the normal equations; it is not an idea
> worthing of a
> publication.
>
> >
> > CHEBYCHEV
>
>
>
> >
> > CR (Conjugate Residuals)
>
> Methods of Conjugate Gradients for Solving Linear Systems, Magnus
> R. Hestenes and Eduard Stiefel,
> Journal of Research of the National Bureau of Standards Vol. 49,
> No. 6, December 1952 Research Paper 2379
> pp. 409--436.
>
> >
> > QCG
>
> The Conjugate Gradient Method and Trust Regions in Large Scale
> Optimization, Trond Steihaug
> SIAM Journal on Numerical Analysis, Vol. 20, No. 3 (Jun., 1983),
> pp. 626-637
>
> >
> > RICHARDSON
>
>
> >
> > TCQMR
>
> Transpose-free formulations of Lanczos-type methods for
> nonsymmetric linear systems,
> Tony F. Chan, Lisette de Pillis, and Henk van der Vorst, Numerical
> Algorithms,
> Volume 17, Numbers 1-2 / May, 1998 pp. 51-66.
> >
> >
> > Could you send me suitable references for these methods?
> >
> > I'm not sure if they exist, but could you also send me suitable
> > references for the following preconditioners:
> >
> > ASM
> An additive variant of the Schwarz alternating method for the
> case of many subregions
> M Dryja, OB Widlund - Courant Institute, New York University
> Technical report
>
> Domain Decompositions: Parallel Multilevel Methods for Elliptic
> Partial Differential Equations,
> Barry Smith, Petter Bjorstad, and William Gropp, Cambridge
> University Press, ISBN 0-521-49589-X.
>
> >
> > BJACOBI
>
> Any iterative solver book, this is just Jacobi's method
> >
> > ILU
> > ICC
> >
>
> Both ICC and ILU the review article
>
> APPROXIMATE AND INCOMPLETE FACTORIZATIONS, TONY F. CHAN AND HENK A.
> VAN DER VORST
>
> http://igitur-archive.library.uu.nl/math/2001-0621-115821/proc.pdf
> chapter in Parallel Numerical
> Algorithms, edited by D. Keyes, A. Semah, V. Venkatakrishnan,
> ICASE/LaRC Interdisciplinary Series in
> Science and Engineering, Kluwer, pp. 167--202.
>
> It is difficult to determine the publications where the FIRST use of
> ILU/ICC appeared since the did not
> call them that originally.
>
> If anyone has references to the original Chebychev and Bi-CG
> algorithms please let us know.
>
> Barry
>
> > Much appreciated
> >
> > Stephen
> > --
> >
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