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Re: References for preconditioners and solver methods.


On Feb 14, 2008, at 12:56 PM, Matthew Knepley wrote:

On Thu, Feb 14, 2008 at 10:30 AM, Stephen R Ball
<Stephen.R.Ball@xxxxxxxxx> 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?

I took at a look at Hestenes and Stiefel, though they don't use the term "conjugate residuals"
I would argue that the algorithm is essentially there and so we should not give
credit to someone else.

   Barry



   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@xxxxxxxxxxx
[mailto:owner-petsc-users@xxxxxxxxxxx] On Behalf Of Barry Smith
Sent: 13 February 2008 20:41
To: petsc-users@xxxxxxxxxxx
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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