BiCGCR2: A new extension of conjugate residual method for solving non-Hermitian linear systems

Article English OPEN
Gu, X-M ; Huang, T-Z ; Carpentieri, B (2016)

In the present paper, we introduce a new extension of the conjugate residual (CR) for solving non-Hermitian linear systems with the aim of developing an alternative basic solver to the established biconjugate gradient (BiCG), biconjugate residual (BiCR) and biconjugate A-orthogonal residual (BiCOR) methods. The proposed Krylov subspace method, referred to as the BiCGCR2 method, is based on short-term vector recurrences and is mathematically equivalent to both BiCR and BiCOR. We demonstrate by extensive numerical experiments that the proposed iterative solver has often better convergence performance than BiCG, BiCR and BiCOR. Hence, it may be exploited for the development of new variants of non-optimal Krylov subspace methods.
  • References (52)
    52 references, page 1 of 6

    [1] T.A. Davis, Direct Methods for Sparse Linear Systems, SIAM Series on the Fundamentals of Algorithms, SIAM, Philadelphia, USA, 2006.

    [2] Y. Saad, Iterative Methods for Sparse Linear Systems, second ed., SIAM, Philadelphia, USA, 2003.

    [3] V. Simoncini, D.B. Szyld, Recent computational developments in Krylov subspace methods for linear systems, Numer. Linear Algebra Appl., 14 (2007), pp. 1-59.

    [4] M.H. Gutknecht, Lanczos-type solvers for nonsymmetric linear systems of equations, Acta Numer., 6 (1997), pp. 271-397.

    [5] R. Barrett, M. Berry, T.F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H.A. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (2nd Edition), SIAM, Philadelphia, USA, 1994.

    [6] M.R. Hestenes, E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Standards, 49 (1952), pp. 409-436.

    [7] X.-M. Gu, M. Clemens, T.-Z. Huang, L. Li, The SCBiCG class of algorithms for complex symmetric systems with applicationsin several electromagnetic model problems, Comput. Phys. Commun., 191 (2015), pp. 52-64.

    [8] C. Paige, M. Saunders, Solution of sparse indefinite systems of linear equations, SIAM J. Numer. Anal. 12 (1975), pp. 617-629.

    [9] E. Stiefel, Relaxationsmethoden bester Strategie zur Lo¨sung linearer Gleichungssysteme, Comment. Math. Helv., 29 (1955), pp. 157-179.

    [10] S.F. Ashby, T.A. Manteuffel, P.E. Saylor, A taxonomy for conjugate gradient methods, SIAM J. Numer. Anal., 27 (1990), pp. 1542-1568.

  • Metrics
    0
    views in OpenAIRE
    0
    views in local repository
    95
    downloads in local repository

    The information is available from the following content providers:

    From Number Of Views Number Of Downloads
    Institutional Repository - IRUS-UK 0 95
Share - Bookmark