Parallel solution of symmetric positive definite systems based on decomposition into overlapping blocks

Computational Mathematics and Mathematical Physics

Volumn 41, Issue 4, 2001, Pages 481-493

  Kaporin, I E ^a   Kon'Shin, I N ^a  

^a RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0142020052     PISSN: 09655425     EISSN: 15556662     Source Type: Journal    
DOI: None     Document Type: Article

References (14)

1. Kaporin, I.E., On the Preconditioning and Parallelization of the Conjugate Gradient Method, in Vvedenie v parallel'nye i vektornye metody resheniya lineinykh sistem, Moscow: Mir, 1990 (a supplement to the Russian edition of Introduction to Parallel and Vector Solution of Linear Systems by J.M. Ortega, New York: Plenum, 1988), pp. 343-355.
2. Kaporin, I.E., New Convergence Results and Preconditioning Strategies for the Conjugate Gradient Method, Numer. Linear Algebra Appl., 1994, vol. 1, no. 2, pp. 179-210.
3. TU-Decomposition, Numer. Linear Algebra Appl., 1998, vol. 5, no. 5, pp. 484-509.
4. Axelsson, O. Lindskog, G., On the Rate of Convergence of the Preconditioned Gradient Methods, Numer. Math., 1986, vol. 48, no. 5, pp. 499-523.
5. Axelsson, O., A Class of Iterative Methods for Finite Element Equations, Computer Meth. Appl. Mech. Eng., 1976, vol. 9, no. 2, pp. 123-137.
6. Kaporin, I.E., Explicitly Preconditioned Conjugate Gradient Method for the Solituon of Unsymmetric Linear Systems, Int. J. Comput. Math., 1992, vol. 40, pp. 169-187.
7. Axelsson, O., Iterative Solution Methods, Cambridge: Cambridge Univ. Press, 1994.
8. Kaporin, I.E., Preconditioning of the Conjugate Gradient Method in Solving Discrete Analogues of Differential Problems, Diff. Uravn., 1990, vol. 26, no. 7, pp. 1225-1236.
9. Kaporin, I.E., Evaluation of Spectra under Two-Sided Explicit Preconditioning, Vestn. Mosk. Gos. Univ., Ser. 15: Vychisl. Mat. Kibern., 1993, vol. 2, pp. 28-42.
10. Tismenetsky, M., A New Preconditioning Technique for Solving Large Sparse Linear Systems, Linear Algebra Appl., 1991, vols. 154-156, pp. 331-353.
11. O'Leary, D.P., The Block Conjugate Gradient Algorithm and Related Methods, Linear Algebra Appl., 1980, vol. 29, pp. 293-322.
12. Kaporin, I.E. and Konshin, I.N., Parallel Solution of Large Sparse SPD Linear Systems Based on Overlapping Domain Decomposition, Parallel Computing Technologies, Malyshkin, V., Ed., Berlin: Springer-Verlag, 1999, pp. 436-445.
13. Benzi, M., Kouhia, R., and Tuma, M., An Assessment of Some Preconditioning Techniques in Shell Problems, Tech. Rep., Los Alamos National Lab., Los Alamos, NM, 1997, LA-UR-97-3892.
14. Karypis, G. Kumar, V., Multilevel k-Way Hypergraph Partitioning, Tech. Rep., no. 98-036, Dept. of Computer Sci. Eng., Army HPC Res. Center, Univ. of Minnesota, Minneapolis, MN, 1998.