References for preconditioners and solver methods.

Thu Feb 14 12:56:30 CST 2008

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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