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: [email protected] [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 > -- > ________________________________________________________________________ _______ > > The information in this email and in any attachment(s) is commercial > in confidence. If you are not the named addressee(s) or if you > receive this email in error then any distribution, copying or use of > this communication or the information in it is strictly prohibited. > Please notify us immediately by email at > admin.internet(at)awe.co.uk, and then delete this message from your > computer. While attachments are virus checked, AWE plc does not > accept any liability in respect of any virus which is not detected. > > AWE Plc > Registered in England and Wales > Registration No 02763902 > AWE, Aldermaston, Reading, RG7 4PR > -- _______________________________________________________________________________ The information in this email and in any attachment(s) is commercial in confidence. If you are not the named addressee(s) or if you receive this email in error then any distribution, copying or use of this communication or the information in it is strictly prohibited. Please notify us immediately by email at admin.internet(at)awe.co.uk, and then delete this message from your computer. While attachments are virus checked, AWE plc does not accept any liability in respect of any virus which is not detected. AWE Plc Registered in England and Wales Registration No 02763902 AWE, Aldermaston, Reading, RG7 4PR
