References for preconditioners and solver methods.

[Stephen R Ball]

Hi

So to clarify then I should use reference:

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.

For both CG and CR?

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: 14 February 2008 19:03
To: petsc-users at mcs.anl.gov
Subject: EXTERNAL: 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 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?

   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 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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