Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 752651, 8 pages
http://dx.doi.org/10.1155/2014/752651
Research Article

Parallel Algorithm with Parameters Based on Alternating Direction for Solving Banded Linear Systems

1Department of Applied Mathematics, Xidian University, Xi’an 710071, China
2Department of Applied Mathematics, Xianyang Normal University, Xianyang 712000, China
3Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China
4School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, China

Received 3 December 2013; Accepted 30 January 2014; Published 7 April 2014

Academic Editor: Massimo Scalia

Copyright © 2014 Xinrong Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. Zhang, T. Gu, and Z. Mo, Principles and Methods of Numerical Parallel Computation, National Defence Industry Press, 1999.
  2. Q. Lü and T. Ye, “An improve parallel algorithm for solving linear equations involving block tridiagonal coefficient matrix,” Journal of Northwestern Polytechnical University, vol. 4, no. 2, pp. 314–317, 1996. View at Google Scholar · View at Scopus
  3. J. Wu, J. Song, W. Zhang, and X. Li, “Parallel incomplete factorization preconditioning of block tridiagonal linear systems with 2-D domain decomposition,” Chinese Journal of Computational Physics, vol. 26, no. 2, pp. 191–199, 2009. View at Google Scholar · View at Scopus
  4. Z. Duan, Y. Yang, Q. Lv, and X. Ma, “Parallel strategy for solving block-tridiagonal linear systems,” Computer Engineering and Applications, vol. 47, no. 13, pp. 46–49, 2011. View at Google Scholar
  5. Y. Fan, The Parallel Algorithms for Solving the Large Scale Linear Systems with Typical Structure, Northwestern Polytechnical University Press, Xi’an, China, 2009.
  6. Z.-G. Luo and X.-M. Li, “Parallel algorithm for block-tridiagonal linear systems on distributed-memory multicomputers,” Chinese Journal of Computers, vol. 23, no. 10, pp. 1028–1034, 2000. View at Google Scholar · View at Scopus
  7. S. M. El-Sayed, “A direct method for solving circulant tridiagonal block systems of linear equations,” Applied Mathematics and Computation, vol. 165, no. 1, pp. 23–30, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  8. X. Cui and Q. Lü, “A parallel algorithm for block-tridiagonal linear systems,” Applied Mathematics and Computation, vol. 173, no. 2, pp. 1107–1114, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  9. R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ, USA, 1962. View at MathSciNet
  10. J. Hu, Iterative Method of Linear Algebraic Equations, Science Press, Beijing, China, 1999.
  11. A. Frommer and D. B. Szyld, “Weighted max norms, splittings, and overlapping additive Schwarz iterations,” Numerische Mathematik, vol. 83, no. 2, pp. 259–278, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  12. J. Feng, G. Che, and Y. Nie, Principle of Numerical Analysis, Science Press, Beijing, China, 2002.
  13. P. Bjørstad and M. Luskin, Parallel Solution of Partial Differential Equations, Springer, New York, NY, USA, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  14. W. H. Reed and T. R. Hill, “Triangle mesh methods for the Neutron transport equation,” Report LA-UR-73-479, Los Alamos Scientific Laboratory, 1973. View at Google Scholar
  15. Y. P. Cheng, Matrix Theory, Northwestern polytechnical University Press, 2002.