Research

Inexact inverse subspace iteration with preconditioning applied to non-Hermitian eigenvalue problems


Reference:

Robbé, M., Sadkane, M. and Spence, A., 2009. Inexact inverse subspace iteration with preconditioning applied to non-Hermitian eigenvalue problems. SIAM Journal On Matrix Analysis and Applications (SIMAX), 31 (1), pp. 92-113.

Related documents:

[img]
Preview
PDF (Spence_SIMAX_submitted.pdf) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (422kB) | Preview

    Official URL:

    http://dx.doi.org/10.1137/060673795

    Abstract

    Convergence results are provided for inexact inverse subspace iteration applied to the problem of finding the invariant subspace associated with a small number of eigenvalues of a large sparse matrix. These results are illustrated by the use of block-GMRES as the iterative solver. The costs of the inexact solves are measured by the number of inner iterations needed by the iterative solver at each outer step of the algorithm. It is shown that for a decreasing tolerance the number of inner iterations should not increase as the outer iteration proceeds, but it may increase for preconditioned iterative solves. However, it is also shown that an appropriate small rank change to the preconditioner can produce significant savings in costs and, in particular, can produce a situation where there is no increase in the costs of the iterative solves even though the solve tolerances are reducing. Numerical examples are provided to illustrate the theory.

    Details

    Item Type Articles
    CreatorsRobbé, M., Sadkane, M. and Spence, A.
    DOI10.1137/060673795
    Uncontrolled Keywordseigenvalue approximation, inverse subspace iteration, preconditioning, iterative methods
    DepartmentsFaculty of Science > Mathematical Sciences
    RefereedYes
    StatusPublished
    ID Code168

    Export

    Actions (login required)

    View Item

    Document Downloads

    More statistics for this item...