References for preconditioners and solver methods.

[Barry Smith]

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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>
>
>
> -- 
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>