Abstract
Efficient use of CG on shared memory multiprocessors requires the detailed examination and testing of the algorithm and its preconditioners as well as the development of innovative approaches to preconditioning. In some cases these approaches lead to improved algorithms even for sequential machines.
Work supported by grants NSF-MIP-8410110, DOE DE-FG02-85ER25001, AT&T-AFFL-67-SAMEH, NSF-CCR-8717942, AFOSR-85-0211, and Digital Equipment Corp.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
W. Abu-Sufah and A. Malony, Experimental results for vector processing on the Alliant FX/8, CSRD Tech. Rept. 539, Center for Sueprcomputing Research and Development, Univ. Illinois-Urbana, (1986).
O. Axelsson and V. Eijkhout, Robust vectorizable preconditioners for three-dimensional elliptic difference equations with anisotrophy, Algorithms and Applications on Vector and Parallel Computers (Ed. H.J.J. te Riele, Th.J. Dekker and H.A. van der Vorst), Elsevier Science Publishers, 1987, pp.279–306.
A. Björck, T. Elfving, Accelerated projection methods for computing pseudo-inverse solutions of systems of linear equations, BIT, 145–163, 19(1979).
R. Bramley, Row projection methods for linear systems, CSRD Tech. Rept. 881, Center for Supercomputing Research and Development, Univ. Illinois-Urbana, (1989).
R. Bramley, A. Sameh, A robust parallel solver for block tridiagonal systems, CSRD Tech. Rept. 806, Center for Supercomputing Research and Development, Univ. Illinois-Urbana, (1988).
P. Concus, G. Golub, and G. Meurant, Block preconditioning for the conjugate gradient method, SIAM J. Sci. Stat. Comput., vol. 6, pp. 220–252, (1985).
Hsin-Chu Chen and Ahmed Sameh, A domain decomposition method for 3D elasticity problems, Applications of Supercomputers in Engineering: Fluid Flow and Stress Analysis Applications (Ed. C.A. Brebbia and A. Peters), Computational Mechanics Publications, Southampton University, UK, Sep. 1989, pp.171–188.
Hsin-Chu Chen and Ahmed Sameh, A matrix decomposition method for orthotropic elasticity problems, SIAM Journal on Matrix Analysis and Applications, vol. 10, No. 1, pp.39–64, Jan. 1989.
Hsin-Chu Chen, The SAS domain decomposition method for structural analysis, CSRD Tech. Rept. 754, Center for Supercomputing Research and Development, Univ. Illinois-Urbana, (1988).
S. Kaczmarz, Angenäherte Auflösung von Systemen linearer Gleichungen, Bull. intern. Acad. polonaise Sci. lettres (Cracouie); Class sci. math. natur.: Seira A. Sci. Math., 355–357 (1939).
C. Kamath, Solution of nonsymmetric systems of equations on a multiprocessor, CSRD Tech. Rept. 591, Center for Supercomputing Research and Development, Univ. Illinois-Urbana, (1986).
C. Kamath, A. Sameh, A projection method for solving nonsymmetric linear systems on multiprocessors, Parallel Computing, 291–312, vol. 9 (1988/1989).
G. Meurant, The block preconditioned conjugate gradient algorithm on vector computers, BIT, vol. 24, pp. 623–633, (1984).
U. Meier and A. Sameh, The behavior of conjugate gradient algorithms on a multivector processor with a hierarchical memory, J. Comp. App. Math., pp. 13–32, vol. 24, (1988).
J. Meijerink and H. van der Vorst, An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix, Math. Comput. 31(137), pp. 148–162, 1977.
Y. Saad, Practical use of polynomial preconditionings for the conjugate gradient method, SIAM J. Sci. Stat. Comput, vol. 6, pp. 865–881, (1985).
H. van der Vorst, The performance of Fortran implementations for preconditioned conjugate gradients on vector computers, Parallel Computing, vol. 3, pp. 49–58, (1986).
H. van der Vorst, ICCG and related methods for 3D problems on vectorcomputers, Report No. A-18, Data Processing Center, Kyoto University, Kyoto, Japan (1987).
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag
About this paper
Cite this paper
Bramley, R., Chen, HC., Meier, U., Sameh, A. (1990). On some parallel preconditioned CG schemes. In: Axelsson, O., Kolotilina, L.Y. (eds) Preconditioned Conjugate Gradient Methods. Lecture Notes in Mathematics, vol 1457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090899
Download citation
DOI: https://doi.org/10.1007/BFb0090899
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53515-7
Online ISBN: 978-3-540-46746-5
eBook Packages: Springer Book Archive