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PARALLEL IMPLEMENTATION OF HYBRID ITERATIVE METHODS FOR NONSYMMETRIC LINEAR SYSTEMS

Yun, Jae-Heon  
  • 초록

    In this paper we study efficient parallel implementation for hybrid iterative methods BICGSTAB and BICGSTAB $(\ell)$ with ${Well}=2$ on the CRAY C90 and the efficiency of their parallel performance is evaluated. numerical experiments suggest that on the CRAY C90 a parallel inner product algorithm called PDOTB be used for the par-allelization of hybrid iterative methods containing sensitive values of inner products. Lastly it is shown that the number of iterations in which parallel hybrid iterative methods satisfy a certain convergence criterion depends on the number of processors to be used.


  • 주제어

    Hybrid iterative methods .   BiCGSTAB .   parallelization .   synchronization .   speedup.  

  • 참고문헌 (9)

    1. J. J. Dongarra;I. S. Duff;D. C. Sorensen;H. A. Van der Vorst , Solving linear systems on vector and shared memory computers / v.,pp.,
    2. BiCGSTAB(ℓ) for linear equations involving unsymmetric matrices with complex spectrum , G. Sleijpen;P. R. Fokkema , ETNA / v.1,pp.11-32,
    3. Conjugate gradient methods for indefinite systems, in Numerical Analysis Dundee 1975 , R. Fletcher;G. A. Watson(ed.); , Lecture Notes in Mathmatics 506 / v.,pp.73-89,
    4. Cray Research , Autotasking User's Guide(SN-2088) / v.,pp.,
    5. R. Barrett(et al.) , Templates for the solution of Linear systems: Building blocks for iterative methods / v.,pp.,
    6. Methods of conjugate gradients for solving innear systems , M. R. Hestenes;E. L. Stiefel , J. Res. Nat. Bur. Standards / v.49,pp.409-436,
    7. GMRES: a generalized minimal residual algorithm for solving nonsymmetric lenear systems , Y. Saad;M. H. Schultz , SIAM J. Sci. Statist. Comput. / v.7,pp.856-869,
    8. Variants of BiCHSTAM for matrices with comples spectrum , M. H. Gutknecht , SIAM J. Sci. Comput. / v.14,pp.1020-1033,
    9. BiCGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems , H. A. Van der Vorst , SIAM J. Sci. Statist. Comput. / v.13,pp.631-644,

 저자의 다른 논문

  • Yun, Jae-Heon (28)

    1. 1993 "A Numerical Method for the Minimum Norm Solution to the First Kind Integral Equations" 충청수학회지 = Journal of the Chungcheong Mathematical Society 6 (1): 25~43    
    2. 1994 "EFFICIENT PARALLEL ITERATIVE METHOD FOR SOLVING LARGE NONSYMMETRIC LINEAR SYSTEMS" Communications of the Korean Mathematical Society = 대한수학회논문집 9 (2): 449~465    
    3. 1994 "Numerical Computation for the Least Squares Solution of Minimum Norm to the First Kind Integral Equations" 충청수학회지 = Journal of the Chungcheong Mathematical Society 7 (1): 97~107    
    4. 1995 "ON THE M-SOLUTION OF THE FIRST KIND EQUATIONS" Communications of the Korean Mathematical Society = 대한수학회논문집 10 (1): 235~249    
    5. 1995 "CONVERGENCE AND BREAKDOWN STUDY OF KRYLOV METHODS FOR NONSYMMETRIC LINEAR SYSTEMS" Communications of the Korean Mathematical Society = 대한수학회논문집 10 (4): 981~995    
    6. 1995 "BCG-LIKE METHODS FOR SOLVING NONSYMMETRIC LINEAR SYSTEMS" 충청수학회지 = Journal of the Chungcheong Mathematical Society 8 (1): 55~69    
    7. 1997 "Performance analysis of a flexible restarted fom(k) algorithm" Bulletin of the Korean Mathematical Society = 대한수학회보 34 (4): 667~678    
    8. 1998 "GENERALIZED STATIONARY ITERATIVE METHOD FOR SOLVING LINEAR SYSTEMS" Korean journal of computational & applied mathematics 5 (2): 383~392    
    9. 1998 "A BLOCKED VARIANT OF THE CONJUGATE GRADIENT METHOD" 충청수학회지 = Journal of the Chungcheong Mathematical Society 11 (1): 129~142    
    10. 1999 "PARALLEL BLOCK ILU PRECONDITIONERS FOR A BLOCK-TRIDIAGONAL M-MATRIX" Journal of the Korean Mathematical Society = 대한수학회지 36 (1): 209~227    
  • Kim, Sang-Wook (9)

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