References for preconditioners and solver methods.

[Stephen R Ball]

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.

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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