Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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PARALLEL BLOCK ILU PRECONDITIONERS FOR A BLOCK-TRIDIAGONAL M-MATRIX

  • Yun, Jae-Heon (Department of Mathematics College of Natural Sciences Chungbuk National University) ;
  • Kim, Sang-Wook (Department of Mathematics College of Natural Sciences Chungbuk National University)
  • Published : 1999.01.01
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Abstract

We propose new parallel block ILU (Incomplete LU) factorization preconditioners for a nonsymmetric block-tridiagonal M-matrix. Theoretial properties of these block preconditioners are studied to see the convergence rate of the preconditioned iterative methods, Lastly, numerical results of the right preconditioned GMRES and BiCGSTAB methods using the block ILU preconditioners are compared with those of these two iterative methods using a standard ILU preconditioner to see the effectiveness of the block ILU preconditioners.

Keywords

References

  1. J. Comput. Appl. Math. v.12;13 Incomplete block matrix factorization preconditioning methods. The ultimate answer? O. Axelsson
  2. Linear Algebra Appl. v.74 A general incomplete block -matrix factorization method O. Axelsson
  3. Iterative solution methods O. Axelsson
  4. Linear Algebra Appl. v.77 on approximate factorization methods for block-matrices suitable for vector and parallel processors O. Axelsson;B. Polman
  5. Templates for the solution of linear systems: Buliding blocks for iterative methods R. Barreett(et al.)
  6. SIAM J. Numer. Anal. v.24 On sparse block factorization, iterative methods R. Beauwens;M. Bouzid
  7. SIAM J. Sci. Stat. Comput. v.6 Block preconditioning for the CG method P. Concus;G. H. Golub;G. Meurant
  8. BIT v.26 On computing INV block preconditioning for the conjugate gradient method P. Concus;G. Meurant
  9. Lecture Notes Math. v.206 Conjugate gradient methods for indefinite systems R. Fletcher
  10. Matrix Computations(3rd edition.) G. H. Golub;C. F. Van Loan
  11. Ph. D. Dissertation, Chungbuk National University Block ILU factorization preconditioners for a block-tridiagonal M-matrix and a generalized variant of stationary iterative method Sang W. Kim
  12. Math. Comput. v.31 An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix J. A. Meijerink;H. A. van der Vorst
  13. BIT v.24 The block preconditioned conjugate gradient method on vector computer G. Meurant
  14. Iterative methods for sparse linear systems Y. Saad
  15. SIAM J. Sci. Statist. Comput. v.7 GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems Y. Saad;M. H. Schultz
  16. SIAM. J. Sci. Statist. Comput. v.10 CGS, a fast Lanczos-type solver for nonsymmetric linear systems P. Sonnerveld
  17. SIAM. J. Sci. Statist. Comput. v.13 Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems H. A. Van der Vorst
  18. J. Comput. Appl. Math. v.94 Block incomplete factorization preconditioners for a symmetric block-tridiagonal M-matrix Jae H. Yun